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已知椭圆C: eqId15bfbddeee0143e08c809ecf76ffb129的左,右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8且椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上的点eqIdd7be5abad1e34f6db17a56660de8d54feqIdab022e7999ae40638fb893499fbc63c2eqId5f04473e64c141bcbe9b0a8af27f4aa8两点的距离之和为4
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)若直线eqId4610b8c449bb4c1ea8495b323539e6bc与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqId71891062a8724584af9a2c4c77cd566e两点,eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点直线eqId0c829d3d33b342c89ac18d70ce316f54的斜率之积等于eqId62db1d1f989e4c4da063e07a8ae90dd7,试探求△OMN的面积是否为定值,并说明理由
更新:2020/04/05 难度:0.4 题型:解答题 组卷:978
已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3:eqId15bfbddeee0143e08c809ecf76ffb129的左、右焦点分别为eqId5f04473e64c141bcbe9b0a8af27f4aa8,离心率为eqId5f816d038c584dc7a249120298677ef3,直线eqId417e80f1349244878d01fe90e0891f5feqIdbd7573e1dfa74982ae46a8861bdd1f50与椭圆交于eqId71891062a8724584af9a2c4c77cd566e,四边形eqId01e0ecae7b05464fa6097ea09bf8247a的面积为eqIdddbb016c3fc24d01bd409b83a9ec5036.
(Ⅰ)求eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(Ⅱ)作与eqId417e80f1349244878d01fe90e0891f5f平行的直线与椭圆交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点,且线段eqId99a3187c2b8f4bcc9703c74c3b72f1f3的中点为eqIdd7be5abad1e34f6db17a56660de8d54f,若eqIdf4aaf7080eae4393ae590699560b8230的斜率分别为eqId67aae67f8f18439e8c51ebb0260bd192,求eqIda129fc6162884ebe8587b7dfcdb51cfe的取值范围.
更新:2020/04/05 难度:0.4 题型:解答题 组卷:1054
已知椭圆eqId211c15b061ee47039dccbca908ea32b4上一点eqId33e512517c164e65b1f204f8d19b9ec6与椭圆右焦点的连线垂直于eqId8e15963708e9415da25069fea5906e24轴,过椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上一点eqIdbedf755e0fdb4d078d6859360706b163的直线eqIda810f6fc814b40e597aa293c65198382与椭圆eqIdc0b463cae1f4448b83bd8435ae28b1a4交于eqIdeb53cb7cb0274f7d8f111c60f824c243两点(eqIdeb53cb7cb0274f7d8f111c60f824c243均不在坐标轴上),设eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,过eqId2efda802d5534f6d92d9f8af7aaec28b的射线eqIda668e52822264c18a05bbdd44d38eb84与椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a交于点eqId75a143b898e14ccdb032561fba9da811
(1)若eqIdbbe8cb480013401387743eadcbb25088,求实数eqId5f420ef2d0b94c4b8a5d8e20a5d1ce2c的值;
(2)当eqIdbedf755e0fdb4d078d6859360706b163eqId33e512517c164e65b1f204f8d19b9ec6时,若四边形eqIda3cc8025e72c49f9b7d1acc399f89a0b的面积为12,试求直线eqId417e80f1349244878d01fe90e0891f5f的方程.
更新:2020/04/05 难度:0.65 题型:解答题 组卷:0
已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的两个焦点分别为eqIde1c38dd1d2684a6a8269de8fafb85f5e,长轴长为eqId7bcd573cee334383ad72cc4b179fcfb3
(Ⅰ)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程及离心率;
(Ⅱ)过点eqId787fec3796eb4e9983c24c49d247da44的直线eqId417e80f1349244878d01fe90e0891f5f与椭圆eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,若点eqId2381423d4cd146cab95f55527681a766满足eqId5be145de0f074a76b1aa78b30cef62cc,求证:由点eqId2381423d4cd146cab95f55527681a766 构成的曲线eqIdfc3da0d522324433b7d5fb46712ec757关于直线eqId02f0e31729cf49fca0916a110ec27862对称.
更新:2020/04/04 难度:0.65 题型:解答题 组卷:809
如图,eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e分别是椭圆CeqIdd448b721bc2f41f8bed63e9521739ce3eqIde9c1eda3dc0c4304868ea148d833743f)的左、右焦点,A是椭圆C的顶点,B是直线eqIdc15e066ad1de447fbfd798b8a945f52c与椭圆C的另一个交点,eqIdead4fefd86d34b28aee25a2fb999b4a5.
figure
(1)求椭圆C的离心率;
(2)已知eqId41a2775e02494ad18583bf6199298068的面积为eqIdf7739e839e2a42578d27a62216b7e512,求ab的值.
更新:2020/04/04 难度:0.65 题型:解答题 组卷:0
已知椭圆eqId44eec5d313e14529946ed1149c870cff的离心率为eqId5f816d038c584dc7a249120298677ef3,以椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的长轴和短轴为对角线的四边形的面积为eqId03859367a9b64a56ab90e31a0cec909a.
(1)求椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a的方程;
(2)若直线eqIdc83501dd60f344529381f122ee6d8215与椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a相交于eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,设eqIdbedf755e0fdb4d078d6859360706b163为椭圆eqId93cbffaa5ae045d6ac45d1e979991c3a上一动点,且满足eqId9a39469e6f344f24b4c76a7de52718bceqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点).当eqIdd124dc511ef84681a9fd3c651894a133时,求eqId3a4208e0040c42ed8b09de2cae9d562e的最大值.
更新:2020/04/04 难度:0.4 题型:解答题 组卷:0
已知椭圆 eqId84904244c3184d5d94f3731c27956a74的左、右顶点分别为eqIdeb53cb7cb0274f7d8f111c60f824c243,点eqIdd7be5abad1e34f6db17a56660de8d54f为椭圆eqId19a4eb16029e4550a14f2afe4741a3c3上不同于eqIdeb53cb7cb0274f7d8f111c60f824c243两点的动点,若直线eqId6f782d71f5a7422aa78bd8204949ce26斜率的取值范围是eqId37209e6461cb412b9d2375994bbcd3bd,则直线eqIde9b50933e347462ea824ccc9bf51fc93斜率的取值范围是(     )
A.eqId932bc8e3bb1947de8d5dba28be85ec23B.eqId5f196b0733f0412f92730ab3a5890022C.eqId91ffc7b8882c4b11872785f6f7cedd9dD.eqIdd3e87113f72d481a933c6195fe36a315
更新:2020/04/04 难度:0.65 题型:单选题 组卷:638
已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdf18b5700afd748c9af08fbce0977010b经过两点eqIdec480cb866604dea9f986c3d5f775487eqId4ede9e663ce6442598508718a8b778d1.
(Ⅰ)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(Ⅱ)过椭圆的右焦点eqId63db14a5b4334f3ea583c8fb12b0d175的直线eqId417e80f1349244878d01fe90e0891f5f交椭圆eqId19a4eb16029e4550a14f2afe4741a3c3eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且直线eqId417e80f1349244878d01fe90e0891f5f与以线段eqIdf5eda07194804949880294807864f832为直径的圆交于另一点eqId93cbffaa5ae045d6ac45d1e979991c3a(异于点eqId63db14a5b4334f3ea583c8fb12b0d175),若eqIda64fb3017bc444309644d6264fa334da,求直线eqId417e80f1349244878d01fe90e0891f5f的斜率.
更新:2020/04/04 难度:0.65 题型:解答题 组卷:0