2022年2019届高考数学考前归纳总结复习题2 .pdf
圆锥曲线中的最值问题一、常见基本题型：（1）利用基本不等式求最值，例 1、已知椭圆两焦点1F、2F在y轴上，短轴长为2 2，离心率为22，P是椭圆在第一象限弧上一点，且121PFPF，过 P作关于直线F1P 对称的两条直线PA、PB分别交椭圆于 A、B两点，求PAB面积的最大值。解、设椭圆方程为22221yxab，由题意可得2,2,2 2abc，故椭圆方程为22142yx设AB的 直 线 方 程：mxy2.由142222yxmxy，得0422422mmxx，由0)4(16)22(22mm，得2222mP到AB的距离为3|md，则3|3)214(21|212mmdABSPAB2)28(81)8(8122222mmmm。当且仅当22,222m取等号，三角形PAB面积的最大值为2。（2）利用函数求最值，例 2.如图，椭圆222:12xyCa的焦点在 x 轴上，左右顶点分别为1,A A，上顶点为 B，抛物线12,C C分别以 A,B 为焦点，其顶点均为坐标原点O，1C与2C相交于直线2yx上一点 P.（1）求椭圆 C及抛物线12,C C的方程；（2）若动直线l与直线 OP垂直，且与椭圆 C交于不同的两点 M,N，已知点(2,0)Q，求QM QN的最小值.解：（1）由题意(,0),(0,2)A aB，故抛物线 C1 的方程可设为axy42，C2的方程为yx242由xyyxaxy224422得)28,8(,4 Pa所以椭圆C:121622yx，抛物线C1：,162xy抛物线C2：yx242（2）由（1）知，直线 OP的斜率为2，所以直线l的斜率为22设直线l方程为bxy22由bxyyx22121622，整理得0)168(28522bbxx因为动直线l与椭圆C 交于不同两点，所以0)168(2012822bb文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3解得1010b设 M（11,yx）、N（22,yx），则2121282816,55bxxb x x58)(2221)22)(22(2221212121bbxxbxxbxbxyy因为),2(),2(2211yxQNyxQM所以2)(2),2)(,2(2121212211yyxxxxyxyxQNQM5141692bb因为1010b，所以当98b时，QNQM取得最小值其最小值等于938514)98(516)98(592例3、已知抛物线)0(2:2ppyxC的焦点为F，抛物线上一点A的横坐标为1x)0(1x，过点A作抛物线C的切线1l交x轴于点D，交y轴于点Q，交直线:2ply于点M，当2|FD时，60AFD（1）求证：AFQ为等腰三角形，并求抛物线C的方程；（2）若B位于y轴左侧的抛物线C上，过点B作抛物线C的切线2l交直线1l于点P，交直线l于点N，求PMN面积的最小值，并求取到最小值时的1x值解：(1)设),(11yxA，则切线AD的方程为pxxpxy2211，文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3所以),0(),0,2(11yQxD，12|ypFQ，所以|FAFQ，所以AFQ为等腰三角形且D为AQ中点，所以AQDF，60,2|AFDDF，12,60pQFD，得2p，抛物线方程为yx42（2）设)0(),(222xyxB，则B处的切线方程为22222xxxy由)4,2(42422121222211xxxxPxxxyxxxy，)1,22(14211211xxMyxxxy同理)1,22(22xxN，所以面积212211221221116)4)()41)(2222(21xxxxxxxxxxxxS设AB的方程为bkxy，则0b由044422bkxxyxbkxy，得代入得：bbkbbbbkS2222)1(64)44(1616，使面积最小，则0k，得到bbbS2)1(令tb，由得ttttttS12)1()(322，文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3222)1)(13()(ttttS，所以当)33,0(t时)(tS单调递减；当),33(t)(tS单调递增，所以当33t时，S取到最小值为9316，此时312tb，0k，所以311y，即3321x。二、针对性练习 1、已知椭圆22:14xGy.过点(,0)m作圆221xy的切线l交椭圆 G于 A,B 两点.将|AB|表示为 m的函数，并求|AB|的最大值.解：由题意知，|1m.当1m时，切线l的方程为1x，点 A,B 的坐标分别为33(1,),(1,)22，此时|3AB；当1m时，同理可得|3AB；当1m时，设切线l的方程为()yk xm.由22()14yk xmxy得22222(1 4)8440kxk mxk m.设 A,B 两点的坐标分别为1122(,),(,)x yxy.文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3又由l与圆221xy相切，得2|11kmk，即2221mkk.所以222221212112|()()(1)()4ABxxyykxxx x42222222644(44)(1)(1 4)14k mk mkkk24 3|3mm.由于当1m时，|3AB，24 3|4 3|233|mABmmm，当且当3m时，|2AB.所以|AB|的最大值为 2.2.如图，DPx轴，点 M在 DP的延长线上，且|2|DMDP当点 P 在圆221xy上运动时。（I）求点 M的轨迹 C的方程；（）过点22(0,)1Tty作圆x的切线l交曲线C于 A，B两点，求AOB 面积 S的最大值和相应的点 T的坐标。解:设点M的坐标为yx,，点P的坐标为00,yx，则0 xx，02yy，所以xx0，20yy，因为00,yxP在圆122yx上，所以12020yx将代入，得点M的轨迹方程 C的方程为1422yx（）由题意知，1|t当1t时，切线l的方程为1y，点A、B 的坐标分别为文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3),1,23(),1,23(此时3|AB，当1t时，同理可得3|AB；当1t时，设切线l的方程为,mkxyRk由,14,22yxtkxy得042)4(222tktxxk设 A、B两点的坐标分别为),(),(2211yxyx，则由得：222122144,42ktxxkktxx又由l与圆122yx相切，得,11|2kt即.122kt所以212212)()(|yyxxAB4)4(4)4(4)1(222222ktktkk.3|342tt因为,2|3|343|34|2ttttAB且当3t时，|AB|=2，所以|AB|的最大值为 2 依题意，圆心O到直线 AB的距离为圆122yx的半径，所以AOB面积1121ABS，当且仅当3t时，AOB面积 S的最大值为 1，相应的T的坐标为3,0或者3,03.已知焦点在y轴上的椭圆 C1：2222bxay=1 经过 A(1，0)点，且离心率为23 (I)求椭圆 C1的方程；文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3 ()过抛物线 C2：hxy2(h R)上 P点的切线与椭圆 C1交于两点M、N，记线段 MN与 PA的中点分别为 G、H，当 GH与y轴平行时，求 h 的最小值解：（）由题意可得222211,3,2.bcaabc，解得2,1ab，所以椭圆1C的方程为2214yx.（）设2,P t th，由2yx，抛物线2C在点P处的切线的斜率为2x tkyt,所以MN的方程为22ytxth代入椭圆方程得2224240 xtxth,化简得222224 1440txt th xth又MN与椭圆1C有两个交点，故422162240thth设1122,Mx yN xy，MN中点横坐标为0 x，则2120222 1t thxxxt,设线段PA的中点横坐标为312tx,由已知得03xx即22122 1t thtt，显然0t,11htt文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y7K10 ZC7B9L1A4V3文档编码:CR4A8X3S9I1 HR4N1I9Y
