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上海市民立中学2018-2019学年高二上学期期末数学试题
上海 高二 期末 2019-12-05 114次

一、填空题添加题型下试题

1. 直线eqIdb545805bdae44bc4b4d7e1264caead7f斜率为__________.
2. 过点eqId2533866b2a4e4c2e9fe68cf94529ee5f且与向量eqId1b74ac6dcf674a5c9e854c773e834b51平行的直线eqId417e80f1349244878d01fe90e0891f5f的方程为__________
3. 直线eqId41858597dd3e43f08a144ae9c433acdd与直线eqId989187bc73e9422d9cb34fa032047f51的夹角eqId8f762f544ae244449c5444fd5645e256__________.
5. 已知椭圆eqId19a4eb16029e4550a14f2afe4741a3c3的参数方程是eqIdf07ada1c6818437ea64a372ce81d2687(eqIdf9db0aee08264a238b9741675591065e为参数,eqId8674597c025f4364bf9ef6b1f34c28dc),则其右焦点坐标是__________.
6. 方程eqIdbdd7950ef54c4b91b2c3983896cc2b2c表示圆,则实数eqId70a27b6ddf6b478285353abb3b1f3741的取值范围是__________.
7. 若eqId8e15963708e9415da25069fea5906e24eqIda96c35333bce498fac43d585fdcaf8c2,且满足约束条件eqId83273534fba748f98e03d94a580d0adf,则eqId2a997e250b2c41738a20f4b2dbafe8c5的最大值为__________.
10. 关于曲线eqIdcd5063ae09384eae814b78a7ef0c0b8d,有如下结论:
①曲线eqId19a4eb16029e4550a14f2afe4741a3c3关于原点对称;
②曲线eqId19a4eb16029e4550a14f2afe4741a3c3关于坐标轴对称;
③曲线eqId19a4eb16029e4550a14f2afe4741a3c3是封闭图形;
④曲线eqId19a4eb16029e4550a14f2afe4741a3c3不是封闭图形,且它与圆eqId789db0c91fdb4cbab79f0a59259ad33f无公共点;
⑤曲线eqId19a4eb16029e4550a14f2afe4741a3c3与曲线eqId4cec4561e7e8422e907576e7785d9639eqIdddd35c5d043e4ebeac32a99367053c68个交点,这eqIdddd35c5d043e4ebeac32a99367053c68点构成正方形.其中有正确结论的序号为__________.

二、单选题添加题型下试题

11. eqIdd7be5abad1e34f6db17a56660de8d54f是椭圆eqIdd0d187826fac4d60ade1ecd61e2a357b上一动点,则点eqIdd7be5abad1e34f6db17a56660de8d54f到椭圆左焦点的最远距离是(   )
A.eqIdddd35c5d043e4ebeac32a99367053c68B.eqId8f65c930571d4ff6aa6a50029d46826eC.eqIddd4bf187d3fd47f6bcc24e568e09643eD.eqId37705e1ef6a84bbdbe88433e75932cdf
12. 方程eqId114ca60d76be4263a82b78615efce225表示双曲线,则实数eqId3a4208e0040c42ed8b09de2cae9d562e的取值范围是(   )
A.eqId6ff20df70312437685576e7405c536afB.eqId23d68d6ba6564137823f6801b7f19026C.eqId394ed81a846d4766a4d7b62cfe12629cD.eqIdfd24b2152eb0437ebeee67e52b357654eqId30bec09073784521830b0b16e03315fd
13. 直线eqId9653aede662045849a68b0f7c3c94480的倾斜角是(     )
A.eqIdc0cb1d8865b74babbf8c4ba2b510a872B.eqId1a446185b2dc4ecb91b191f89532b2aaC.eqId04fbea62f95e4b7c9beb22f39b89304aD.eqId5a2eb1637a0848b18f81591f65b36303
同步
14. 平直角坐标系内,到点eqIdbe973624835548d9b3b266400250beba和直线eqId223b251e8f154fadaa2a7c63161a754e距离相等的点的轨迹是(   )
A.直线B.椭圆C.双曲线D.抛物线

三、解答题添加题型下试题

15. 已知直线eqIdb4cd09f502c44700995c61eb7f6fcd6e被圆eqId9e484b39235641c28c9d2b4ef6e16b8c所截得的弦长为eqId401586f7a7f248b7904a4cfeaa2ed2f0,求eqIdaea992e70d4943e49e893817eb885ed7的值.
16. 已知两条直线eqIdc526aa03ab9b4f1cbd86c207ea1f65d5eqId4caf3b94de1844c7bf1b193a73239f3b,当eqId70a27b6ddf6b478285353abb3b1f3741为何值时
(1)eqId74c7e0292b094e54ae596d37798a05edeqId439fb93f7745417b8bb1747d963c6e60垂直;
(2)eqId74c7e0292b094e54ae596d37798a05edeqId439fb93f7745417b8bb1747d963c6e60平行.
17. 已知中心为原点,焦点在坐标轴上的双曲线eqId19a4eb16029e4550a14f2afe4741a3c3经过点eqId3c825ae4672046238adddb44415acccf,它的一条渐近线的程为eqId051de20bc1a84059b5b75b38b736b3bf.
(1)求双曲线的标准方程;
(2)过双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的点eqId0aa72756ed0c4c7a89f26aa94f43e47d垂直于实轴的直线eqId417e80f1349244878d01fe90e0891f5f,在第一象限与双曲线相交点eqIdbedf755e0fdb4d078d6859360706b163eqIdde963a24921f4ee7a991bf9d4f43a42e为双曲线eqId19a4eb16029e4550a14f2afe4741a3c3的另一个焦点,求eqIda0630b0433694e2c93052b19dec269c6的面积.
18. 已知抛物线eqIdd050af449075401299cc78c647d310e8的焦点为eqId63db14a5b4334f3ea583c8fb12b0d175,点eqIdcc614bd3390c4d028df189b234dcc351是抛物线eqId19a4eb16029e4550a14f2afe4741a3c3上的动点.
(1)求动点eqIdcc614bd3390c4d028df189b234dcc351到点eqIdf61dd628c7904baabc45b820b80163e3的距离的最小值;
(2)若点eqIdcc614bd3390c4d028df189b234dcc351eqIdbedf755e0fdb4d078d6859360706b163满足eqId1930c110d2f246c6a826628bf5bbc0ef,当点eqIdcc614bd3390c4d028df189b234dcc351在抛物线eqId19a4eb16029e4550a14f2afe4741a3c3上运动时,求动点eqIdbedf755e0fdb4d078d6859360706b163的轨迹方程.
19. 已两动圆eqIde6c6aa9d38da4a54ac3aee983bc30013eqId13671e4acf4a4439bf19e118bd5410f8eqIddaed6b90f16a4ee18ca3fc1c7ba15ce4,把它们的公共点的轨迹记为曲线eqId19a4eb16029e4550a14f2afe4741a3c3,若曲线eqId19a4eb16029e4550a14f2afe4741a3c3eqId072d7d6b911b42bc89207e72515ebf5f轴的正半轴交点为eqId2381423d4cd146cab95f55527681a766,且曲线eqId19a4eb16029e4550a14f2afe4741a3c3上异于点eqId2381423d4cd146cab95f55527681a766的相异两点eqIdcc614bd3390c4d028df189b234dcc351eqId8754ce8cf7f34f04abb9a0c041f57f5c满足eqId9af3905831674d29adfde871d66b9ca9.
(1)求曲线eqId19a4eb16029e4550a14f2afe4741a3c3的方程;
(2)证明直线eqId99a3187c2b8f4bcc9703c74c3b72f1f3恒经过一定点,并求出此定点的坐标.