名校
解题方法
1 . 已知椭圆
:
,直线
与椭圆
交于
,
两点,以线段
为直径的圆经过原点.若椭圆
的离心率不大于
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-03-04更新
|
764次组卷
|
5卷引用:2020届湖南省长沙市长郡中学高三上学期月考(四)数学(理)试题
名校
解题方法
2 . 已知椭圆
:
的离心率为
,左、右顶点分别为
、
,过左焦点的直线
交椭圆
于
、
两点(异于
、
两点),当直线
垂直于
轴时,四边形
的面积为6.
(1)求椭圆的方程;
(2)设直线
、
的交点为
;试问
的横坐标是否为定值?若是,求出定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)求椭圆的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2020-02-19更新
|
492次组卷
|
2卷引用:湖南省长沙市开福区第一中学2019-2020学年高二上学期第二次阶段性考试数学试题
名校
3 . 已知中心为原点O,焦点在x轴上的椭圆C的离心率为
,且椭圆C的长轴是圆
的一条直径.
(1)求椭圆C的方程;
(2)若不过原点的直线l与椭圆C交于A,B两点,与圆M交于P、Q两点,且直线OA,AB,OB的斜率成等比数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5240a75b910e7d57c991cd574ee896e3.png)
(1)求椭圆C的方程;
(2)若不过原点的直线l与椭圆C交于A,B两点,与圆M交于P、Q两点,且直线OA,AB,OB的斜率成等比数列,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b1113864968119e61aeee9ba9c613b.png)
您最近一年使用:0次
名校
4 . 在平面直角坐标系
中,已知
、
分别为椭圆
的左、右焦点,且椭圆
经过点
和点
,其中
为椭圆
的离心率.
(1)求椭圆
的标准方程;
(2)过点
的直线
交椭圆
于另一点
,点
在直线
上,且
,若
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e75072df252fa117c44efb7e0578fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1c0b88aa9154ba9bf7020a4e26fad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aafd69cf859866ab01eee58a9cf09796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2020-02-10更新
|
806次组卷
|
7卷引用:湖南省长沙市长郡中学2018-2019学年高三下学期第六次月考数学(文)试题
5 . 已知椭圆
,倾斜角为60°的直线与椭圆分别交于A、B两点且
,点C是椭圆上不同于A、B一点,则△ABC面积的最大值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2410a0ca6cd1a408bae14f0dc97553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8379fa789beacfd81edb91e9f795b0.png)
您最近一年使用:0次
2019-12-31更新
|
817次组卷
|
4卷引用:湖南师大二附中2020-2021学年高三上学期第一次阶段性考试数学试题
湖南师大二附中2020-2021学年高三上学期第一次阶段性考试数学试题浙江省宁波市宁波十校2019-2020学年高三上学期11月月考数学试题(已下线)专题16 椭圆的简单几何性质(核心素养练习)-【新教材精创】2020-2021学年高二数学新教材知识讲学(人教A版选择性必修第一册)(已下线)第三章 圆锥曲线与方程(提分小卷)-【单元测试】2021-2022学年高二数学尖子生选拔卷(苏教版2019选择性必修第一册)
名校
6 . 如图,哈尔滨市有相交于点
的一条东西走向的公路
与一条南北走向的公路
,有一商城
的部分边界是椭圆的四分之一,这两条公路为椭圆的对称轴,椭圆的长半轴长为2,短半轴长为1(单位:千米). 根据市民建议,欲新建一条公路
,点
分别在公路
上,且要求
与椭圆形商城
相切,当公路
长最短时,
的长为________ 千米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ccc19a183b9ce7f82d2609a14b9a43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/6a307920-760e-4446-b9ab-6a6ae7c24807.png?resizew=137)
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2019-12-09更新
|
313次组卷
|
5卷引用:湖南省长沙市浏阳市第一中学2019-2020学年高三上学期第六次月考数学(理)试题
名校
7 . 已知椭圆
:
,
,
分别是椭圆短轴的上下两个端点,
是椭圆的左焦点,P是椭圆上异于点
,
的点,若
的边长为4的等边三角形.
写出椭圆的标准方程;
当直线
的一个方向向量是
时,求以
为直径的圆的标准方程;
设点R满足:
,
,求证:
与
的面积之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ed513f56811aa1d314514c5c10d90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef3c9dd64ecdf6d1fc3ab081aeb6a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ed513f56811aa1d314514c5c10d90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef3c9dd64ecdf6d1fc3ab081aeb6a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa117b0621fb0e843929b033a4c09814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f670b461d9b13df3932d0b0eeaea1f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c1bc582e15c8ae375017eff356fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f670b461d9b13df3932d0b0eeaea1f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372ba3183665678900fbed833aabb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9763e9bc0e618b3a6338254410a058c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e25e267418280b37e7d2f0bef11b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e9be82ad7b51f39e8058452b0e87b67.png)
您最近一年使用:0次
2019-11-08更新
|
462次组卷
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6卷引用:2020届湖南省长沙市明达中学高三(高复部)第二次模拟考试理科数学试题
2020届湖南省长沙市明达中学高三(高复部)第二次模拟考试理科数学试题2019年上海市崇明区高三上学期期末(一模)数学试题上海市华东师范大学第三附属中学2019-2020学年高二上学期12月月考数学试题(已下线)专题05 平面解析几何-2020年高三数学(理)3-4月模拟试题汇编(已下线)专题02圆锥曲线全章复习攻略--高二期末考点大串讲(沪教版2020选修一)(已下线)专题02 圆锥曲线--高二期末考点大串讲(沪教版2020选修)
名校
8 . 已知
,
为椭圆
的左、右顶点,
为其右焦点,
是椭圆
上异于
,
的动点,且
面积的最大值为
.
(1)求椭圆
的方程及离心率;
(2)直线
与椭圆在点
处的切线交于点
,当点
在椭圆上运动时,求证:以
为直径的圆与直线
恒相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
您最近一年使用:0次
名校
9 . 已知椭圆中心在原点,焦点在
轴上,离心率
,点
、
分别为椭圆的左、右焦点,过右焦点
且垂直于长轴的弦长为
.
(1)求椭圆的标准方程;
(2)过椭圆左焦点
作直线
,交椭圆于
、
两点,若
,求直线
的倾斜角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆的标准方程;
(2)过椭圆左焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44a1a86c133fc3c25a4997616845eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
10 . 已知椭圆
的上下两个焦点分别为
,过点
与
轴垂直的直线交椭圆
于
两点,
的面积为
,椭圆
的长轴长是短轴长的
倍.
(1)求椭圆
的标准方程;
(2)已知
为坐标原点,直线
与
轴交于点
,与椭圆
交于
两个不同的点,若存在实数
,使得
,求
的取值范围,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5585a42c8f07ad90b94ace9db3d78994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74681aa6901213e672154f38ead0fa6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2019-12-03更新
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748次组卷
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3卷引用:湖南省长沙市宁乡市2022-2023学年高二上学期期末数学试题