组卷网>高中数学综合库>平面解析几何>圆锥曲线>直线与圆锥曲线的位置关系>直线与椭圆的位置关系>求直线与椭圆的交点坐标
题型:解答题 难度:0.4 引用次数:195 更新时间:2021/5/19 16:29:18 题号:12950283
已知椭圆eqId258968a3c695495d93f7f8f57e4dbe94的左顶点为A,过其右焦点F作直线交椭圆CDE(异于左右顶点)两点,直线ADAE与直线eqId83604a8bccb74330aa114f6b5cb85f67分别交于MN,线段MN的中点为H,连接FH.
(1)求证:eqId17f4a9c48e204a808a5a841a67cd4fa4
(2)求eqId3f1bab605c0841e796df60c638114203面积的最小值.

类题推荐

解答题 | 较难(0.4) |
解题方法
【推荐1】如图,在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别为椭圆eqId0cea1b4143794e648461083dfa398706的左、右焦点,动直线eqId417e80f1349244878d01fe90e0891f5f过点eqIdde963a24921f4ee7a991bf9d4f43a42e,且与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点(直线eqId417e80f1349244878d01fe90e0891f5feqId8e15963708e9415da25069fea5906e24轴不重合).
figure
(1)若点eqIdcc614bd3390c4d028df189b234dcc351的坐标为eqIdc709f521150546a29c15d0733dab07d8,求点eqId8754ce8cf7f34f04abb9a0c041f57f5c坐标;
(2)若eqId1f1b13f20df344c4a387a105e2964b71,求eqId9ad43be2f520443a8f3ac415ca76b08d面积的最大值.
更新:2020/04/03组卷:110
解答题 | 较难(0.4) |
解题方法
【推荐2】已知eqId2efda802d5534f6d92d9f8af7aaec28b是坐标原点,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdc5ecf5c8a6a64d7492c7a2876523baed的左、右顶点分别为eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e为其左、右焦点,点eqIdbedf755e0fdb4d078d6859360706b163是椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上异于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c的任意一动点,过点eqIdcc614bd3390c4d028df189b234dcc351作直线eqId0f58df63e3bf4964984d172e7b4ac968轴,eqId75a143b898e14ccdb032561fba9da811为直线eqId417e80f1349244878d01fe90e0891f5f上一点.
(1)若eqId41c6793fbe3d400d89f837b065571453eqIdf95334ee237f468eb6f7b97d394bd72d关于直线eqId091494dd685b40288accb57da94871ae对称,且eqIdc6efdc01592b470197ffaa462a793255eqId2381423d4cd146cab95f55527681a766eqIdf7008eedb7a24975b878d93187c8475e,求eqId4cd2c77f45b74c709061330d26be4e39的面积;
(2)若eqId84deaa1ea0634d9e9a38a7426e2c73f5,证明:eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811eqId8754ce8cf7f34f04abb9a0c041f57f5c三点共线.
更新:2020/07/30组卷:125
解答题 | 较难(0.4) |
压轴
【推荐3】已知椭圆EeqId15bfbddeee0143e08c809ecf76ffb129的离心率eqId5dd2923dcdc745f98f1bb0ad5e9e62d1,焦距为eqId2644c4fd7d684e75ae5ed93cb3581244
eqIdd996f15bd38249f7b7e35e6afefa8c0beqId8fbdf36fcfa44dddb74ad17d601f601d求椭圆E的方程;
eqIdd996f15bd38249f7b7e35e6afefa8c0beqId8fbdf36fcfa44dddb74ad17d601f601dCD分别是椭圆E的左、右顶点,动点M满足eqId84605c3b64874ac6b6670816d10ef340,连接CM,交椭圆E于点eqId41f3feb60447407aa4e3a0bad84910d8证明:eqId5f39a782a9dd41a79751a815a75a6d6d为定值eqIde653506b194641f086281d41fb7393b7为坐标原点eqId8fbdf36fcfa44dddb74ad17d601f601d
更新:2018/07/11组卷:802
3道题,平均难度一般 清空试题 进入组卷中心
收起