名校
1 . 已知方程
表示椭圆,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c06239ad76993ff9491ab4773471d23.png)
A.m的取值范围为![]() | B.若该椭圆的焦点在y轴上,则![]() |
C.若![]() | D.若![]() ![]() |
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2023-02-25更新
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902次组卷
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5卷引用:重庆市万州第二高级中学2022-2023学年高二下学期3月第一次月考数学试题
2 . 定义:若点
在椭圆
上,并满足
,则称这两点是关于
的一对共轭点,或称点
关于
的一个共轭点为
.已知点
在椭圆
上,
是坐标原点.
(1)求点
关于
的所有共轭点的坐标:
(2)设点
在
上,且
,求点
关于
的所有共轭点和点
所围成封闭图形面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15db2e747c8e8aa279ff2dd4905ee0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c60c285f0c38a75bc794ff0f82b009e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5d31d0499d9a6a59600bec270bc6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876869be261bb82f2e0fb02abdcd3107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2998cded64250a90a4c00f2a4e5f72c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
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解题方法
3 . 已知椭圆
的焦点为F1,F2,第一象限的点
为椭圆上的动点,当
为直角三角形时,点
的横坐标是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6205da5e1d2730ee0b3de8bca3e29f5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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4 . 已知椭圆
的上下焦点分别为
,左右顶点分别为
,
是该椭圆上的动点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f642cc82f9cb94f68265b4ec78f8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.该椭圆的长轴长为![]() |
B.使![]() ![]() |
C.若点![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() |
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2022-10-08更新
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1999次组卷
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5卷引用:重庆市第八中学校2022-2023学年高二上学期第一次月考数学试题
5 . 已知椭圆
的左、右焦点分别为
,
,点
在椭圆上,且
,则椭圆的短轴长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929dc77863a9e447ce3e3c956b8b15bf.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/c30ee8b98bd071f65863897db9cbacb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc99276dbd561c9859c88c333f214dcc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 已知
分别是椭圆
的左、右焦点.
(1)若
是第一象限内该椭圆上的一点,且满足
,求点
的坐标;
(2)设过定点
的直线与椭圆交与不同的两点
,且
为锐角,求直线
斜率的平方的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6bb9de257b598c60ae7eab1eb6c06d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设过定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ed90ebf0061c8a79beed307fc1719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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7 . 椭圆
上一点
到左焦点
的距离为6,若点
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d910b176147bd5892bf072c8f2052233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a66a89cfbd291f63855801b081c876.png)
A.6 | B.4 | C.2 | D.![]() |
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2020-02-28更新
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418次组卷
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2卷引用:重庆市巴蜀中学校2018-2019学年高二上学期期末(文)数学试题
名校
8 . 已知
、
分别为椭圆
的左、右焦点,过
作
轴的垂线交椭圆于点
,
与
轴的交点为
,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/cfb7101fa9146fdec51d44b8bf481dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4968a9e1e90a0e9c6c16b42bffba5e4f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-02-24更新
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174次组卷
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2卷引用:重庆市西南大学附属中学2018-2019学年高二上学期期中(理)数学试题