名校
解题方法
1 . 已知椭圆
的左顶点和右顶点分别为
和
,椭圆
的离心率为
并且与直线
相切.
(1)求椭圆
的方程;
(2)若
,
分别为
上两点(不与
,
重合),若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ac01ad57b76eeb3505b9c89141877d6.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/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/14f34b78957c4b554505e54e254d34db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baefc8a9b711ab9f3741491fd298a119.png)
您最近一年使用:0次
2 . 已知椭圆
的离心率为
,且椭圆上一点与椭圆两个焦点构成的三角形的周长为
,
(1)求椭圆
的方程.
(2)设直线
与椭圆交于
两点,若以
为直径的圆经过椭圆的右顶点
,求
的值及
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3643fa70165ed9fef1398bc9443e7a02.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf46f98449e6b3cd06d129d003ae32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
3 . 如图,椭圆
和圆
,已知椭圆C的离心率为
,直线
与圆O相切.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/4449f2dd-e3a8-458c-894c-3ef28ec2c138.png?resizew=173)
(1)求椭圆C的标准方程;
(2)椭圆C的上顶点为B,EF是圆O的一条直径,EF不与坐标轴重合,直线BE、BF与椭圆C的另一个交点分别为P、Q,求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b4bcb812c997db47214cb52c905f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26e366e3d5391b401cf4cd4fc970403.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/4449f2dd-e3a8-458c-894c-3ef28ec2c138.png?resizew=173)
(1)求椭圆C的标准方程;
(2)椭圆C的上顶点为B,EF是圆O的一条直径,EF不与坐标轴重合,直线BE、BF与椭圆C的另一个交点分别为P、Q,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdb8865ae357b7a16b6a30cf4a9e592.png)
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2024-02-06更新
|
131次组卷
|
2卷引用:江西省新余市2023-2024学年高二上学期期末质量检测数学试题卷
名校
解题方法
4 . 已知
,
分别是椭圆
的左、右焦点,如图,过
的直线与C交于点A,与y轴交于点B,
,
,设C的离心率为
,则( )
![](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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4efa339dbb8c7026b0959971349ae18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fd6f15bd77332ca6defccf3ebd65c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2024-02-06更新
|
584次组卷
|
4卷引用:河南省信阳市固始县2023-2024学年高二上学期期末考试数学试卷
名校
解题方法
5 . 已知椭圆
的两焦点分别为
、
,且椭圆的离心率为
.
(1)求椭圆E的方程;
(2)过两焦点的直线分别交椭圆于A,B,C,D四点,若
,求平行四边形ABCD面积最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817e9ed9062ace5344891c1cde6e1c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dcf02e64b9374c513c6bf9c31ad3cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8c94479a04ba31b10af88b677e5057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/81949e67-7526-4492-a15b-bd397004046d.png?resizew=149)
(1)求椭圆E的方程;
(2)过两焦点的直线分别交椭圆于A,B,C,D四点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
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2024-02-05更新
|
1205次组卷
|
3卷引用:江西省上饶市2023-2024学年高二上学期期末教学质量测试数学试题
23-24高二上·广东深圳·期末
解题方法
6 . 已知椭圆
:
的离心率为
,左、右焦点分别为
,
,
为坐标原点,且
.
(1)求椭圆
的方程;
(2)已知过点
的直线
与椭圆
交于
,
两点,点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4f7e7f33963df24d6a46067b4677e5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693d8ab207950adb01f5461171a50634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff9f805576c92e32085c6b8c4a369de.png)
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解题方法
7 . 已知
为椭圆
的两个焦点,过
的直线与C交于M,N两点.若
,
,则C的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b7b8327139b0058a512a8b256f1a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7155f4135d1d728947cb3986675533.png)
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名校
解题方法
8 . 已知椭圆
的左焦点为
,如图,过点
作倾斜角为
的直线与椭圆
交于
两点,
为线段
的中点,若
(
为坐标原点),则椭圆
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211999b4e3e5b24afc5a680b099c1b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
9 . 光线从椭圆的一个焦点发出,被椭圆反射后会经过椭圆的另一个焦点;光线从双曲线的一个焦点发出,被双曲线反射后的反射光线等效于从另一个焦点射出,如左图,一个光学装置由有公共焦点
、
的椭圆
与双曲线
构成,
与
的离心率之比为
,现一光线从左焦点
发出,依次经
与
反射,又回到了点
,历时
秒;若将装置中的
去掉,如图,此光线从点
发出,经
两次反射后又回到了点
,历时
秒,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f686dba2d99ad0c492169ee7f0ee3b8.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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60fe5130254a1d38bb4fd0015630f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f686dba2d99ad0c492169ee7f0ee3b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/4/00d5394b-cf93-4340-ba4b-b6bbf47dac73.png?resizew=350)
您最近一年使用:0次
解题方法
10 . 已知椭圆
过点
,且离心率
.
(1)求椭圆
的方程;
(2)
为椭圆
的右焦点,
为直线
上一点,过点
作
的垂线
交椭圆
于
两点,连接
与
交于点
(
为坐标原点).求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb4e996beb1cf6c93f9d951b0586b7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234e7679481ec0d01c915b7fbb71891d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e2acd4f8b7d0e7797bc2737003d84b2.png)
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