组卷网>知识点选题>待定系数法求双曲线方程
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1 . 双曲线eqIdceed1a7797e443d9abdce2f0c8179d8e的顶点焦点到eqId19a4eb16029e4550a14f2afe4741a3c3的一条渐近线的距离分别为eqIda2a0ce3781fa4c26b624f5966b7dee44eqId7bcd573cee334383ad72cc4b179fcfb3,则eqId19a4eb16029e4550a14f2afe4741a3c3的方程为(   )
A.eqId77f0d42a3e9a4223a32b7a7e4b3e8e7cB.eqIdc59ff4f56d494a72b98b81c9c1660152
C.eqIdb0c1ce39923d4bed9facd6970f8772daD.eqIda9f465d6a4f04a358eaf8bfea615c387
2 . 求适合下列条件的曲线的标准方程:
(1)eqId46189b156f2844f58eb66818ccaf3657,焦点在eqId072d7d6b911b42bc89207e72515ebf5f轴上的双曲线的标准方程;
(2)焦点在eqId072d7d6b911b42bc89207e72515ebf5f轴上,且焦点到准线的距离是2的抛物线的标准方程.
3 . 双曲线eqId9aca4748e10b4a46802f26823a3e28c6eqId982da3835b7946d999cc8604a2ece266)的一条渐近线的方程为eqId7921a304b3094405b788a0db6bde4d22,则双曲线的实轴长为(   )
A.eqId37705e1ef6a84bbdbe88433e75932cdfB.eqId49b7b111d23b44a9990c2312dc3b7ed9C.eqIdc052ddfbd4524f67a79e0e77c2e5656aD.eqId4a6d9e827a244409a8376651b7e648c4
解答题 | 一般(0.65) | 2021·山东高三其他模拟
4 . 已知双曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqIdf5a1cc66e7f343dd9739779f8057b84e的右焦点eqId63db14a5b4334f3ea583c8fb12b0d175与抛物线eqIdaec51f58aebe474ea6639989a83d8f9c的焦点重合,一条渐近线的倾斜角为eqIde284d00e97a84f75a75aa3666a424b22
(1)求双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)经过点eqId63db14a5b4334f3ea583c8fb12b0d175的直线与双曲线的右支交与eqIdeb53cb7cb0274f7d8f111c60f824c243两点,与eqId072d7d6b911b42bc89207e72515ebf5f轴交与eqIdbedf755e0fdb4d078d6859360706b163点,点eqIdbedf755e0fdb4d078d6859360706b163关于原点的对称点为点eqId75a143b898e14ccdb032561fba9da811,求证:eqId6f836511ec514c34b75a27827546455e
解答题 | 较难(0.4) | 2021·湖南高二期中
5 . 已知双曲线eqId811db9dc81da49d983c7d440e851d85e过点eqIdddc40432644c49d0aea802d2c3b3b14f,且该双曲线的虚轴端点与两顶点eqId123f61d182834c79a426dd2e33e1b818的张角为eqId62e24b0e15744029a67505f18ae7806d
(1)求双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a的方程;
(2)过点eqId6850c2eafd704f588b32db96f8cd3856的直线eqId417e80f1349244878d01fe90e0891f5f与双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a左支相交于点eqId71891062a8724584af9a2c4c77cd566e,直线eqIddd5bb4fc741b4a9698da04f10bc23ba5eqId072d7d6b911b42bc89207e72515ebf5f轴相交于eqIdfcf606636c8549158e75f6db78c50096两点,求eqIdcb1310f62de449a7b271a71aa7f2d46e的取值范围.
单选题 | 较易(0.85) | 2020·江苏高三一模
6 . 在平面直角坐标系eqId2272a344734c4fb088737b84294f7219中,若双曲线eqIdf038e982d4c349b6b6d80737045def13经过点eqId76c0449c79a84fe5a33faa7b8bf4623d,则该双曲线的渐近线方程为(   )
A.eqId2747a0a5e7f048c3bea5d78f1368668cB.eqId04fa12fdeab7469b817a7e42f804a494C.eqIdc0b6f6ff6f9c4fb785473ff0c3095d9aD.eqId58c292d6f488439aa41b4b10febb1864
解答题 | 较难(0.4) | 2021·湖南高二期末
7 . 设点eqIdbedf755e0fdb4d078d6859360706b163为双曲线eqIda6d3d00ca52748cd8370b775f1762b6d上任意一点,双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a的离心率为eqIda2a0ce3781fa4c26b624f5966b7dee44,右焦点与椭圆eqId86a000a8e66b47efa8468754abf92016的右焦点重合.
(1)求双曲线eqId93cbffaa5ae045d6ac45d1e979991c3a的标准方程;
(2)过点eqIdbedf755e0fdb4d078d6859360706b163作双曲线两条渐近线的平行线,分别与两渐近线交于点eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5c,求证:平行四边形eqId41d8decac91e40f897bf90a51926a253的面积为定值,并求出此定值.
8 . (1)已知椭圆的长轴长为6,一个焦点为eqIdafed4da885124e6a9b4b7e8d5053b1e3,求该椭圆的标准方程.
(2)已知双曲线过点eqIdfe3d5f70a8704c758b57bf787efd0ace,渐近线方程为eqId5c7e5d7621784c1386a467306fdcd344,求该双曲线的标准方程.
9 . 已知直线eqIdebfe81c073584115a3b2659ed595d2a0被中心在坐标原点,焦点在坐标轴上的双曲线所截得的线段长为6,被该双曲线的两条渐近线截得的线段长为eqId62f2412997424b4ca41272f35d432557,则该双曲线的标准方程为(   )
A.eqIdc59ff4f56d494a72b98b81c9c1660152eqId070295248222419e8fc90991c1d00078B.eqId6fdca2ed1b9b45b9a26bda911b982eb2eqId8cf5e79e23d64e839f694f1f31b013dc
C.eqIdc59ff4f56d494a72b98b81c9c1660152D.eqId8cf5e79e23d64e839f694f1f31b013dc
单选题 | 容易(0.94) |
10 . 已知双曲线C与椭圆eqId91d6f8ce99774242a92b776b08b9051b有共同的焦点,且焦点到该双曲线渐近线的距离等于1,则双曲线C的方程为(   )
A.eqId3ac3abd0255e4f1989a8b2a3d8f26cebB.eqId71fc94555de74fd5b79f98bd4829fb64C.eqId0480be991e024bda8ea70870ae9865a4D.eqId7e6f9468d1ea4cf1b69ebe2ccb200217
更新:2021/06/14组卷:344
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