名校
1 . 已知定圆
,定点
,动圆
满足与
外切且与
内切,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce7ccf9d6206df56cc836f2ac59e052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bea681006f614f8a070e9c6a942c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5f743330edfb013634d7528c607028.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:江西省赣州市2020-2021学年高二上学期期末考试数学(理)试题
2 . 已知椭圆
内有一点
,
为椭圆的左焦点,
是椭圆上的一动点,设
的最大值和最小值分别为
和
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a309c6a2396f84212dbe6ece1a94cfe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b2cc0d2f6d3eee9a33db83e0c0830d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef56c3786eda518cd3dfca9b2e128eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d06ad126eef8c33fdcd8a55107fe7d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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20-21高二上·江苏南通·期末
3 . 已知椭圆
的左、右焦点分别为
、
,点
,若点P为椭圆C上的一个动点,则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2ad383609e51d65a2abfa43f3414d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfd49824c176aa69164bfb91dc0147f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706e0350fd1c36a4e3c66868a8218a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1511c558821b59d783d19ad6c44b8c3e.png)
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名校
解题方法
4 . 历时
天嫦娥五号成功携带月球样品返回地球,标志着中国航天向前迈出一大步.其中
年
月
日晚,嫦娥五号成功进行首次近月制动,进入一个大椭圆轨道.该椭圆形轨道以月球球心为一个焦点
,若其近月点
(离月球表面最近的点)与月球表面距离为
公里,远月点
(离月球表面最远的点)与月球表面距离为
公里,并且
,
,
在同一直线上.已知月球的半径为
公里,则该椭圆形轨道的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f592748753dbbbd747a14a94a2dea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701554763bdbbf2689a8dae07608da38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0b71b8d2c183154221f717ce09077b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbecbd7e92dcbe1766462fcf40066de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2858005b9ae89ae080d83dcc13cf8e81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3e95410f3b4fcb0cba425b521d1f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:山东省济南市2020-2021学年高二上学期期末数学试题
名校
解题方法
5 . 已知椭圆
的左、右两个焦点分别为F1,F2,P为椭圆上一动点,M
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
A.![]() | B.![]() ![]() |
C.存在点P使得![]() | D.![]() |
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10卷引用:广东省深圳市光明区2020-2021学年高二上学期期末数学试题
广东省深圳市光明区2020-2021学年高二上学期期末数学试题(已下线)卷14 选择性必修第一册高二上期中考试 总复习检测5(难)-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)(已下线)卷13 选择性必修第一册高二上期中考试 总复习检测4(中)-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)重庆市合川实验中学2020-2021学年高二下学期开学考试数学试题江苏省南京市第二十九中学2021-2022学年高二上学期10月检测数学试题福建省福州市连江尚德中学等六校2021-2022学年高二上学期期中考数学试题2023版 苏教版(2019) 选修第一册 突围者 第3章 第一节 课时1 椭圆的标准方程江苏省南京市江浦高级中学2022-2023学年高二上学期10月阶段检测数学试题河南省开封市立洋外国语学校2022-2023学年高二上学期期中数学试题云南省临沧市民族中学2022-2023学年上学期高二第三次月考数学试题
解题方法
6 . 若实数x,y满足方程
,则
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fbdcf5ed16ea6ae22fe7446d9aab97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f288b64132d9dbee27d88e97e3df237.png)
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7 . 若实数
,
满足方程
,则
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f4c57826e92e54bd9f3606069191f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f288b64132d9dbee27d88e97e3df237.png)
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8 . 如图所示,在圆锥内放入两个球
,
,它们都与圆锥相切(即与圆锥的每条母线相切),切点圆(图中粗线所示)分别为
,
.这两个球都与平面
相切,切点分别为
,
,丹德林(G·Dandelin)利用这个模型证明了平面
与圆锥侧面的交线为椭圆,
,
为此椭圆的两个焦点,这两个球也称为Dandelin双球.若圆锥的母线与它的轴的夹角为
,
,
的半径分别为1,4,点
为
上的一个定点,点
为椭圆上的一个动点,则从点
沿圆锥表面到达
的路线长与线段
的长之和的最小值是( )
![](https://img.xkw.com/dksih/QBM/2021/1/20/2640312339546112/2642193082179584/STEM/bd78e574-d137-4faa-a932-e63e376d1f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e69fd92eceb49fed10c4b50723d13d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ba050bb69ab55bdcb96f935f5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e69fd92eceb49fed10c4b50723d13d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ba050bb69ab55bdcb96f935f5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f7ba050bb69ab55bdcb96f935f5922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://img.xkw.com/dksih/QBM/2021/1/20/2640312339546112/2642193082179584/STEM/bd78e574-d137-4faa-a932-e63e376d1f9a.png)
A.6 | B.8 | C.![]() | D.![]() |
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名校
9 . 给出下列结论:动点
分别到两定点
,
连线的斜率之积为
,设
的轨迹为曲线
,
分别为曲线
的左、右焦点,则下列命题中:
(1)曲线
的焦点坐标为
,
;
(2)曲线
上存在一点
,使得
;
(3)
为曲线
上一点,
,
,
是一个直角三角形的三个顶点,且
,
的值为
;
(4)设
动点
在曲线
上,则
的最大值为
;
其中正确命题的序号是________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd0825e68122a65426840fbf07cf296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e1bb189df5a70eaca676f99aeb5b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8725396e8316c31c876f9fd08e05083f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40af87a5d4b92c7fb0c898cb0d63fe21.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d5ea72ab40951bee69e26ec50ba15.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727c32b3f38d2e1f464711e1547c1b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e84e3a6855369ad6cb75ad7874f5d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19477696c5f4e42b9347ebc94e54feb7.png)
(4)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdeb51d4c591643b189d102d31648874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bc4513c28444aef25e3b34c3e23974.png)
其中正确命题的序号是
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3卷引用:安徽省阜阳市颍东区衡水实验中学2020-2021学年高二上学期第四次调研考试数学(理)试题
2021高三·山东·专题练习
名校
10 . 已知椭圆
的左、右焦点分别为
,
且
,点
在椭圆内部,点
在椭圆上,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17769176e152f359c7211d1fcedf0d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2644e9f73e5871db934fdafc431d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() ![]() |
B.椭圆![]() |
C.椭圆![]() ![]() |
D.若![]() ![]() ![]() |
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7卷引用:江苏省扬州中学2020-2021学年高二下学期开学考试数学试题
江苏省扬州中学2020-2021学年高二下学期开学考试数学试题苏教版(2019) 选修第一册 突围者 第3章 第一节 课时2 椭圆的几何性质(已下线)专题3.1 椭圆-《讲亮点》2021-2022学年高二数学新教材同步配套讲练(苏教版2019选择性必修第一册)(已下线)期中考试重难点专题强化训练(3)——圆锥曲线的综合运用-2021-2022学年高二数学单元卷模拟(易中难)(2019人教A版选择性必修第一册+第二册)(已下线)热点09 解析几何-2021年高考数学【热点·重点·难点】专练(山东专用)江西省寻乌中学2022-2023学年高二下学期第二次阶段性测试(6月)数学试题(已下线)第十一章 圆锥曲线专练5—椭圆小题最值问题-2022届高三数学一轮复习