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题型:解答题 难度系数:0.4 引用次数:159 更新时间:2019/02/12 04:37:55 题号:7570569
在直角坐标系eqId2272a344734c4fb088737b84294f7219中,椭圆eqIdc3b97a393de447caa56c33f22b32bf2deqIdf18b5700afd748c9af08fbce0977010b的离心率为eqIddb6b28cbd8a14caa9cf1146f6f7916c0,椭圆短轴上的一个顶点为eqId0b8f3954b0d742599fb174f85fb3c91f
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)已知点eqId9abda9b3157e492b9376adc9211927d4,动直线eqIdca2562bc01c14710825ecd4b6cfd2906与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于eqId8e6acd891f5c4ee58e49a1a58ccdf866两点,若直线eqId77af6c3f7ba346e18b62006cc002dc52的斜率均存在,求证:直线eqId55cb7749a1724da4bba612e010232667的斜率依次成等差数列.
类题推荐
【推荐1】已知椭圆eqIdf10e4030482c416bbf7f10fa9d71ff1c的一个焦点eqIdd5b10b2a13f148b78e0d5a1b820538fd与抛物线eqId80dd232d266c4238b3ea4c16db3c7ca1的焦点重合,且eqId2381423d4cd146cab95f55527681a766经过点eqId33e512517c164e65b1f204f8d19b9ec6.
(1)求椭圆eqId2381423d4cd146cab95f55527681a766的方程;
(2)已知斜率大于0且过点eqIdd5b10b2a13f148b78e0d5a1b820538fd的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId2381423d4cd146cab95f55527681a766及抛物线eqId517584fed25c413ba8b7bb33ffa2d5c6自上而下分别交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3eqId0cd8063abf2b458f80091bc51b75a904,如图所示,若eqId223a5d6f8ae0476e837e49a1d4563cad,求eqIdf1b7fd40a322477db7876d3b83d83a1f.figure
难度系数:0.4使用:154次题型:解答题更新:2019/6/27
【推荐2】已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的焦点在坐标轴上,对称中心为坐标原点,且过点eqId41f80a5d158e473fbdeaa84b64c3f425eqIdf5569d7c098f49019b55b5fd36e93a7c.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)设直线eqId417e80f1349244878d01fe90e0891f5f交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId3804465f6d584f2f9bd4e1ad9a3dc087两点,坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b到直线eqId417e80f1349244878d01fe90e0891f5f的距离为eqId9a19f81624ec431494b1feeb88f12bdf,求证:eqIdf6856749cd29470986879c046caece7e是定值.
难度系数:0.65使用:321次题型:解答题更新:2019/7/12
【推荐3】如图,在平面直角坐标系eqIdf6795042a6be4af49cb950f48e99a5ea中,已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId24454b5c394946168d06488b0ff1d83a经过点eqId98afe071d5a94b0591ec1686877f9dea.设椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的左顶点为eqIdcc614bd3390c4d028df189b234dcc351,右焦点为eqIdd5b10b2a13f148b78e0d5a1b820538fd,右准线与eqIdc12aac8c2448479687a40735b3572a23轴交于点eqId2381423d4cd146cab95f55527681a766,且eqIdd5b10b2a13f148b78e0d5a1b820538fd为线段eqId70cd1808ec2941c8b922af637375e79b的中点.
figure
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)若过点eqIdcc614bd3390c4d028df189b234dcc351的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于另一点eqIdd7be5abad1e34f6db17a56660de8d54feqIdd7be5abad1e34f6db17a56660de8d54feqIdc12aac8c2448479687a40735b3572a23轴上方),直线eqId4b82a69b3fbe43a882c29faae5fabff0与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3相交于另一点eqIdca9308a4ebd84ed8a28d8a519a8dbb39,且直线eqId417e80f1349244878d01fe90e0891f5feqId1c09b834da954c89875289069a1b8059垂直,求直线eqId4ea1af672e334fb1a6a3ab675d494e72的斜率.
难度系数:0.65使用:188次题型:解答题更新:2019/6/18
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