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单选题 | 容易(0.94) | 2021·广东高二期末
1 . 已知椭圆eqIdfd8674e21002436f9476310a52d934ec的左右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,离心率为eqIdbf4d8b310ca74c22a7eb63a406f4674a,过eqIdde963a24921f4ee7a991bf9d4f43a42e的直线eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3eqId11ac1550e51640518ac966047848b311两点,若eqId75eb4cc2af0644cfb60bd5564e75f7f1的周长为eqId62f2412997424b4ca41272f35d432557则,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程为(   )
A.eqId15ddf0bba96b4162a10a0bab1fd8a511B.eqIdd43aac02505b4bc6aff2bb19bcb7ae52
C.eqId9fdcf8b3733c488f8f52479762e044d8D.eqId8a2037287af44430b323943afad608ed
2 . 设椭圆CeqIdd448b721bc2f41f8bed63e9521739ce3的左、右焦点为eqId5f04473e64c141bcbe9b0a8af27f4aa8,过点eqIdde963a24921f4ee7a991bf9d4f43a42e的直线lx-y-1=0交CAB两点,eqId937353dd4a3440099a5734703a4d6bf7的周长等于8.
(1)求C的标准方程;
(2)求eqId937353dd4a3440099a5734703a4d6bf7的面积.
3 . 设椭圆eqIdd448b721bc2f41f8bed63e9521739ce3的左、右焦点为eqId5f04473e64c141bcbe9b0a8af27f4aa8,过点eqId0aa72756ed0c4c7a89f26aa94f43e47d的直线与椭圆相交于AB两点,eqIdbe4da2ee7a074b03b16288940dbe918d,则椭圆的离心率是____________.
4 . 已知椭圆eqIdcb94200200f74d65ac6c5aa8bd8a33d7的离心率为eqId5f816d038c584dc7a249120298677ef3,依次连结eqId93cbffaa5ae045d6ac45d1e979991c3a的四个顶点构成的四边形面积为eqId2644c4fd7d684e75ae5ed93cb3581244.
(1)求eqId93cbffaa5ae045d6ac45d1e979991c3a的方程;
(2)设eqId93cbffaa5ae045d6ac45d1e979991c3a的左,右焦点分别为eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42e,经过点eqId58f2b48fbfbf453381ad2e21e05008ba的直线eqId417e80f1349244878d01fe90e0891f5feqId93cbffaa5ae045d6ac45d1e979991c3a交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且eqId016871ceb470449f91e015385d783d89,求eqId417e80f1349244878d01fe90e0891f5f的斜率.
单选题 | 容易(0.94) | 2021·全国高二课时练习
5 . 已知△eqIda670baf5d73f4d7689915a00c51820f2的顶点eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3在椭圆eqIdee68bbcf796743ceb35b5df8defd6cf6上,顶点eqId052844cae8574a8ab842c38a039baac0是椭圆的一个焦点,且椭圆的另外一个焦点在eqId0627be51821d4be7b3e024a354815d64边上,则△eqIda670baf5d73f4d7689915a00c51820f2的周长为(   )
说明: figure
A.eqIdc052ddfbd4524f67a79e0e77c2e5656aB.eqId7bcd573cee334383ad72cc4b179fcfb3
C.eqIdddd35c5d043e4ebeac32a99367053c68D.eqId62f2412997424b4ca41272f35d432557
更新:2021/08/02组卷:0
单选题 | 较易(0.85) | 2021·全国高二课时练习
同步
6 . 在eqId0b4671382ad6491cb648fae82fdffac1中,eqId47becd547d424a6e9a5286e384f92e1f,如果一个椭圆通过eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,它的一个焦点为点eqId19a4eb16029e4550a14f2afe4741a3c3,另一个焦点在eqId99a3187c2b8f4bcc9703c74c3b72f1f3上,则这个椭圆的离心率eqId798d7463abda4e278ad50ee077068a1d(   )
A.eqId4f3c6468b96b42b69860452c387ced32B.eqId59b4960b0bac4e02af68fbea0819706dC.eqId11a75c651d0a45c6a582be841e9561cfD.eqId82746e172282441db6dd51f0df0ce6b6
更新:2021/08/02组卷:0
解答题 | 较易(0.85) | 2021·全国高二课时练习
同步
7 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的中心为原点,焦点eqId0aa72756ed0c4c7a89f26aa94f43e47deqIdde963a24921f4ee7a991bf9d4f43a42eeqIda9cd3f94eb8045438f75e9daccfa7200轴上,离心率为eqId5f816d038c584dc7a249120298677ef3.过eqId0aa72756ed0c4c7a89f26aa94f43e47d的直线eqId417e80f1349244878d01fe90e0891f5feqId19a4eb16029e4550a14f2afe4741a3c3eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且eqId9ac8f5dbc275451280c88a998a64aa89的周长为eqId1c1b006090344679b56b4c75d395cd8e,求椭圆的标准方程.
更新:2021/08/02组卷:0
8 . 已知椭圆eqIdfd8674e21002436f9476310a52d934ec的离心率为eqIde0b8cd3018f64415bea8dce0a25d0538,点eqIdbedf755e0fdb4d078d6859360706b163eqId63db14a5b4334f3ea583c8fb12b0d175分别是其下顶点和右焦点,坐标原点为eqId2efda802d5534f6d92d9f8af7aaec28b,且eqId1cbf3708b36d4679b790e0632488e808的面积为eqId5f816d038c584dc7a249120298677ef3
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)是否存在直线eqId417e80f1349244878d01fe90e0891f5f,使得eqId417e80f1349244878d01fe90e0891f5f与椭圆相交于eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c两点,且点eqId63db14a5b4334f3ea583c8fb12b0d175恰好为eqId1efce4fe353e494795a806b4b87f4b1a的垂心?若存在,求直线eqId417e80f1349244878d01fe90e0891f5f的方程;若不存在,请说明理由.
填空题 | 容易(0.94) | 2021·全国高二课时练习
同步
9 . 已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的焦点在坐标轴上,且经过eqIda1f379731f524e71bcef67457187cb5eeqId1e133de62d9c40b68a242e6286b72d22两点,则椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程为_______.
更新:2021/08/01组卷:0
10 . 已知椭圆eqId76662bc293df4139b90c65ed8b136d3beqId207ddd75d0ee42629ce30bec7dcdaba1)经过点eqIdeddd78e40e304a50bdb1b0f604868d32,且长轴是短轴的两倍.
(1)求椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)设eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点,eqId6cc42e5ac9db4ba2904f529e9cbb6c0d,直线eqIddabdc1cf868d44d2ac7b5ce4e9d68f9feqId69822b73f6db46e6918e6051ce01567d)与曲线eqId19a4eb16029e4550a14f2afe4741a3c3交于eqIdbedf755e0fdb4d078d6859360706b163eqId75a143b898e14ccdb032561fba9da811两点,直线eqId6dc069fc1fa74d889be09b5324e7e625eqIda9cd3f94eb8045438f75e9daccfa7200轴相交于点eqId2381423d4cd146cab95f55527681a766,直线eqId0c43edec1bef4ede93a413694f6f5d55eqIda9cd3f94eb8045438f75e9daccfa7200轴相交于点eqId517584fed25c413ba8b7bb33ffa2d5c6,若eqIdfc944e4cc0f540779470331dea65b49e,求证:直线eqId417e80f1349244878d01fe90e0891f5f经过定点.
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