高中数学题库-平面解析几何初步

高中数学题库-平面解析几何初步 1. 直线方程 (一)直线的位置关系 ,,y,321. 已知集合，，若 A,(x,y),a，1,,B,(x,y)(a,1)x，(a,1)y,15,,x,2,, A:B,,，则的值为____________________ a ,32(若直线与直线平行，则 ( m,2x，(m，1)y，4,0mx，3y，4,0 3. 已知m,{,1，0，1}，n,{,1，1}，若随机选取m，n，则直线恰好不经mxny，，,10过第二象限的概率是 ( xy，?3，,,122y?3，4(已知实数，满足约束条件则的最大值为 ( xzxy,,,5y,2,x?3，, ,5. 已知两条直线的斜率分别为，设的夹角(锐角)为. l,lk,k(0,k,k)l,l12121212 k,k21tan,(1)求证:, 1，kk12 ,(2)求直线与直线的夹角 2x,y，1,0x,3y,3,0 226. 求函数的最小值. y,x,2x，5，x,4x，13 227. 求函数的最小值. y,x，4x，13,x,2x，5 22x,2，y,2,18. 若，则的最大值为_______. x，y 2ll9. 已知直线过不同的两个点，，则直线的倾斜角的取值范围是B(0,1)A(cos,,sin,) ,,3,，，,___________. 0,:,,,,,,44,，，, (二)直线应用题 0OMONOAOB，,MON601. 如图所示，有两条道路与，，现要铺设三条下水管道，， integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, OMON3km(其中，分别在，上)，若下水管道的总长度为，设，ABABOAakm,() ( OBbkm,() b(1)求关于的函数 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 达式，并指出的取值范围; aa (2)已知点处有一个污水总管的接口，PN 3OM点P到的距离为，到点PHkmB4b P7OPO的距离为，问下水管道km4 PAB能否经过污水总管的接口点,若 Oa能，求出的值，若不能，请说明理由( aHAM解:建系，检验是否三点共线即可 2. 如图在矩形ABCD中，已知AB=3AD，E，F为AB的两个三等分点，AC，DF交于点G( ,(?)建立适当的平面直角坐标系，证明:EGDF; (?)设点E关于直线AC的对称点为,,，问点是否在直线DF上，并说明理由( EE 证明:(?)如图，以AB所在直线为x轴，以AD所在直线为y轴建立直角坐标系，设AD长度为1， 则可得，，，， ( „„„„„„„2分 A(0,0)D(0,1)E(1,0)F(2,0)C(3,1) 1所以直线AC方程为，? yx,3 1直线DF方程为，? „„„„„„„ 4分 yx,,，12 62由??解得交点 ( „„„„„„„ 6分 G(,)55 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 1?EG斜率，又DF斜率， k,,k,2DFEG2 ?，即有EGDF( „„„„„„„ 8分 ,kk,,,1EGDF xy，111,,(?)设点，则中点M， EEExy(,)(,)1122 yx，11,11,,,,232, 由题意得 „„„„„„„ 11分 ,y11,,,,1,,x,131, 43解得( „„„„„„„ 14分 ,E(,)55 314 ?， ,,,，()1525 ?点在直线DF上( „„„„„„„ 16分 ,E 3. 如图，O为总信号源点，A，B，C是三个居民区，已知A，B都在O的正东方向上， 52OA = 10 ，OB = 20 ，C在O的北偏西45? 方向上，CO =( kmkmkm(1)求居民区A与C的距离; (2)现要经过点O铺设一条总光缆直线EF(E在直线OA的上方)，并从A，B，C分别铺设三条最短分光缆连接到总光缆EF(假设铺设每条分光缆的费用与其长度的平方成正比，比例系数为m(m为常数)(设?AOE = θ(0?θ <)，铺设三条分光缆的总费用为wπ (元)( ? 求w关于θ的函数表达式; 北 tan,? 求w的最小值及此时的值( C E θ ABO F(第18题) integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 在平面直角坐标系中，直角梯形AOBC的位置如图所示，?OAC,90?，AC?OB，OA,4，AC,5，OB,6(M、N分别是线段AC、线段BC上的动点，当?MON的面积最大且周长最小时，点M的坐标为 _______ . 2. 圆的方程 221. 在平面直角坐标系中，已知直线与圆交于xOy360xy，,,(3)(1)2xy,，,, ,OAOB，两点，则直线与直线的倾斜角之和为 ( AB3 ,,xy222. 已知集合,若AxyxyBxyab,，,,，,,,(,)1,(,)1,0,0xyR,,,,,,,ab,, AB:只有一个元素，则应满足的关系为__________ ab, 222MNM:,r,0MxyxyNxyxyr,，,,，,(,)1,(,)3. 已知，集合，若，,,,, 2，1则的最大值为______________;若则的最小值为_____________ MNN:,,rr2 22P4. 已知圆与直线相交于，Q两点，若 yx,3Cxayaa:()()1(0),，,,, 0a,，则实数 ( ，,PCQ90 0变式1 “”改为所求三角形CPQ面积最大，则实数a=_____. ，,PCQ90 000变式2“”中90改为60，则实数a=________. ，,PCQ90 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 0变式3“”中“=”改为“<”，则实数a的取值范围为__________. ，,PCQ90 5. 一类存在性问题探究 kk例:(2013年苏锡常镇徐连一模)若对于给定的正实数，函数的图像上总存 fx(),x CCOk在点，使得以为圆心，1为半径的圆上有两个不同的点到原点的距离为2，则的 取值范围是 2k920,k,解法1:可转化为双向不等式的有解问题，即，解得: 1,x，,322x 92k,90,k,解法2:可利用图像研究其充要条件为:，解得: 2 22原型:(2012年江苏高考题)在平面直角坐标系中，圆C的方程为，xOyxyx，,，,8150若直线上至少存在一点，使得以该点为圆心，1为半径的圆与圆C有公共点，则ykx,,2 k的最大值是 _____________ 6. 已知圆C的内接正方形相对的两个顶点的坐标分别为，( A(1,1),B(3,5)(?)求圆C的方程; (?)若过点M的直线l与圆C有且只有一个公共点，求直线l的方程. (2,0), 解:(?)由题意得圆心， „„„„„„ 2分 C(2,2) RAC,,10 半径， „„„„„„ 4分 22 所以圆C的方程为( „„„„„„ 6分 (2)(2)10xy,，,, (?)显然直线l不可能垂直x轴，设直线l的方程为， ykx,，(2) 因为直线l与圆C有且只有一个公共点， |222|kk,，所以圆心到直线的距离， „„„„„„ 9分 d,,102k，1 1k,3k,, 解得或( „„„„„„ 12分 3 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 所以直线l的方程为或( „„„„„„ 14分 360xy,，,xy，，,320 222227. 若圆与圆相交，则实数m的取值范围xymm，,,(0)xyxy，，,,,68110 为 ((1，11) 22228. 在直角坐标系xOy中，已知A(,1，0)，B(0，1)，则满足且在圆PAPB,,4xy，,4 上的点P的个数为 ( 2 229. 在平面直角坐标系xOy中，圆C:关于直线l:对xy，,,250xyxy，,,，,481901 22称的圆C的方程为 ( xy，,12 2 2 210. 已知圆O的方程为x， y, r(r为正的常数)， 设P(m，n)为平面内的一个定点，求证:存在定点 MPQ，使得对圆O上的任意一点M，均有为定值( MQ 222211. 已知，且，求证:. 圆构成的区域的包x,y,Rx，y，2y,0x，y，6x，8,0含关系. 2x2，,y112. 在平面直角坐标系xOy中，已知椭圆的左、右焦点分别为F ,与F，圆:F4 22xy,，,35( ，， ,,,,,,,,,,(1)设M为圆F上一点，满足，求点M的坐标; MF'MF,,1 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, (2)若P为椭圆上任意一点，以P为圆心，OP为半径的圆P与圆F的公共弦为QT， 证明:点F到直线QT的距离FH为定值( y QF 'OF x H P T (第17题) 3. 动态问题研究 221. 已知圆M:，过轴上的点存在一直线与圆M相交，交xPa(,0)(1)(3)4xy,，,, 点为A、B，且满足PA=BA，则点P的横坐标的取值范围为 ( a 222,MCmr，,,CMCABm,2ABMP解:取中点，连接、，设则 相减得,222MCmMP，,3，，,, 22222222？0,,mrMPmrm,，,，884MPm,，,8436， ?，即 (1)336a,，, y133133,,,，a? B ( M A Pox 222222. 已知A = { (x，y) | x ， y ?4 }，B = { (x，y) | (x , a) ， (y , a)?2a，a , 0 }，则A?B表示区域的面积的取值范围是___________((0，2π) xNMNMyex,,13. 分别在曲线与直线上各取一点与，则的最小值为 ( ye, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 1 2e，1 专题思考:两条曲线，两个动点问题的研究很不容易;所以研究这类问题我们的想法是能不能先定一个点，只研究一个动点问题; 1x变式1:(2012年新课标全国理科卷)设点在曲线上，点在曲线Py,eQy,ln(2x)2 上，则的最小值为____________ 两函数互为反函数; PQ2(1,ln2) 22yx22变式2:在椭圆与圆各取一点M,N，则MN的最小值为_____ ，,1(x,1)，y,142 6，1 3y,变式3:已知是双曲线图像上两点，则MN的最小M(x,y),N(x,y),xx,0112212x 26值为___________. 改编自2011年江苏高考题:在平面直角坐标系中，过坐标原点的一条直线与函数xoy 2fx,，，的图象交于两点，则线段长的最小值为 P,QPQx 背景:在双曲线中，两个实轴顶点间的距离为所求最小值 变式4:如果是函数图像上的点，是函数图像上的点，且M,N两 NMy,g(x)y,f(x) y,f(x)点之间的距离能取到最小值d，那么将d称为函数与之间的距离. MNy,g(x) 72,1按这个定义，函数和之间的距离是 g(x),,x，4x,3f(x),x2 xOyPab(,)yx,,，24. 在平面直角坐标系中，若动点到两直线l:和l:的距离 yx,12 2222ab，之和为，则的最大值为 ( 18 a,b，a，b,2,4解:由题意得: a,b,a,b,,, ,,2222a，b,2,a，b,2,ab，ab，(1)此时的最大值为;(2)此时的最大值为10; 18,, ,,a,3.a,,1.,, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, a,b,a,b,,, ,,2222a，b,2,a，b,2,(3)此时ab，的最大值为10;(4)此时ab，的最大值为. 18,, ,,b,,1.b,3.,, 225. 在平面直角坐标系中，已知圆O:，点，M，N为圆O上不同的xOyP(1,2)xy，,16 ,,,,,,,,,,,,,,,,,,,,,,,,,,两点，且满足(若，则的最小值为 ( PMPN,,0335,PQPMPN,，PQ 22PR，OR,16RPQ,2PR妙解:，由题意得，可得点所在的轨迹方程为: 12722()(1)x,，y,,，可得最小值 24 222226. 已知A = { (x，y) | x ， y ?4 }，B = { (x，y) | (x , a) ， (y , a)?2a，a , 0 }，则A?B表示区域的面积的取值范围是___________( 2 27. 已知圆C:x， y , 1，点P(x，y)在直线x , y , 2 , 0上，O为坐标原点，若圆C上存00 在点Q，使?OPQ , 30:，则x的取值范围是 ( 0 axbyc，，,08. 已知实数a，b，c成等差数列，点P( , 1，0)在动直线上的射影为M，点N(2，1)，则线段MN长的取值范围是____________( 122P(,1)9. 过点的直线l与圆交于A，B两点，当?ACB最小时，直Cxy:(1)4,，,2 integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 线l的方程为 ( ,,,,,,,,10. 点P为单位圆O外的一点，PA，PB为圆O的两条切线，则的最小值为 ( PAPB, 22n,R11. 设m，，若直线与圆相切，则的最大值是(1)+(1)2=0mxny,,，xy+=1mn+_________. 1y,12. 曲线C:与轴的交点关于原点的对称点称为“望点”，以“望点”为圆心，y||1x, 凡是与曲线C有公共点的圆，皆称之为“望圆”，则“望圆”面积的最小值为 ( x222Fxyxy(,)()(),,，，13. 设，对于一切x，y?，y?0，的最小值为________( Fxy,R，，2y 42214. 已知集合，，Bxyxy,,，,,{(,)|2|3||4|},Axyxy,,，,,{(,)|(3)(4)}5 AB:,,,若，则实数的取值范围是__________. ,,422,(,)(,1)，(,2),变式:(2008浙大自主招生)已知集合， Axyxy,,5,, A,Ba,2，若，则实数的取值范围是_______. ,,B,(x,y)x,1，2y,2,aa 22215. 在平面直角坐标系中，已知点在圆内， xOyP(3,0)Cxymxym:24280，,,，,, AB,C16动直线过点且交圆于两点，若?ABC的面积的最大值为，则实数的取 mPAB 值范围为 ( [323,327)(327,323]，，,,: 讲评建议:设圆心角为θ，α<=θ<180度，则„„，所以α<=90度. 则弦长小于等于4，圆心距大于等于4，又„„ 2216. 设t?R，[t]表示不超过t的最大整数(则在平面直角坐标系xOy中，满足[x]+[y]=13 的点P(x，y)所围成的图形的面积为 (8( 解:本题主要考查运用所学知识 分析 定性数据统计分析pdf销售业绩分析模板建筑结构震害分析销售进度分析表京东商城竞争战略分析 问题与解决问题的能力( 22 先考察点当x?0，y?0的情形(由[x]+[y]=13，得 []2,x,[]3,x,23,,,x34,,,x,,,, 所以， ,,,,34,,,y23.,,y[]3,y,[]2.y,,,,, 从而，当x?0，y?0时，P(x，y)所围成的图形的面积为2( 其次，由对称性，点P在坐标平面内所围成的图形面积为4×2=8( integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, 2222 可求解下列变式题:变[x]+[y]=13为[x]+[y]=25，则面积为16( C17. 在平面直角坐标系中，分别是轴和轴上的动点，若以为直径的圆与直AByxA,B C线相切，则圆面积的最小值为__________. 4π/5 2x，y,4,0 【解】以为直径的圆过坐标原点，则原点到直线距离即为圆直径的最小值. AB integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the city's liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the country's first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for "water and the second land of the seven hills". 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, "old town-the South Bank" Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, "suspicious" pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed,