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1 . 直线
与双曲线
的两条渐近线交于
两点,
分别为双曲线的左、右焦点.
(1)求过点
的圆的方程;
(2)设(1)中的圆和双曲线在第一象限交于点
,求圆在点
处的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7638c88f01d609d79947033ed4ff36a2.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea98501007b43f9e3253d4ae91a1ae9.png)
(2)设(1)中的圆和双曲线在第一象限交于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-02-18更新
|
92次组卷
|
2卷引用:山东省菏泽市2023-2024学年高二上学期期末教学质量检测数学试题
2 . 已知双曲线E:
与直线l:
相交于A、B两点,M为线段AB的中点.
(1)当
时,求双曲线E的左焦点到直线l的距离;
(2)若l与双曲线E的两条渐近线分别相交于C、D两点,问:是否存在实数k,使得A、B是线段CD的两个三等分点?若存在,求出k的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892b7c3cd7bea116f532f66fba44662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9db6ebe391887fccaf3916e9f57cab.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e26838e7dbb6febf2fc04db05893a4.png)
(2)若l与双曲线E的两条渐近线分别相交于C、D两点,问:是否存在实数k,使得A、B是线段CD的两个三等分点?若存在,求出k的值;若不存在,说明理由.
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3 . 已知曲线C:
(
且
)的左、右焦点分别为
,
,直线
与
交于点
,
.
(1)若
,且四边形
是矩形,求
的值;
(2)若
是
上与
,
不重合的点,且直线
,
的斜率分别为
,
,若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb783f89d6c82bb0b59f6f28e669dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663acb9ca61a9d102de6d9ea5144601b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.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/ac02a054bd0771a56987af33454baaea.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)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfffd420523729074995e9e55f464d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76edc10b8d1df1db5fa8f1c1c780bc3e.png)
(2)若
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1231f7ed4ee750149db85d8fe614ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdfc6a59392d1ac3cd89ddc0308864c.png)
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2024-01-29更新
|
173次组卷
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2卷引用:安徽省部分学校2023-2024学年高二上学期期末检测数学试题
4 . 已知双曲线
.
(1)求上焦点
的坐标;
(2)若动点
在双曲线的上支上运动,求点
到
的距离的最小值,并求此时
的坐标;
(3)若
为双曲线的上顶点,直线
与双曲线交于C、D两点(异于点
),
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ddacb9233c23d3c83c8d9cff313d669.png)
(1)求上焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(2)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3325d357e4e3a160e6cc357cac2c1543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4147f37263dc5cdebcf9d53b758977dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf6e750ebbb7b47b17d1c4f21be76d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2024-01-20更新
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248次组卷
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2卷引用:上海市莘庄中学2023-2024学年高二上学期期末数学试题
5 . 求双曲线C:
的焦点坐标、实轴长、虚轴长、渐近线方程和离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff70ebf6fe1445882fa79762f39b0d7c.png)
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6 . 求双曲线
的实半轴长和虚半轴长、焦点坐标、离心率、渐近线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6aeaa05d6032fb4aebbeefdc2e5022.png)
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7 . 求双曲线
的实轴和虚轴长,焦点和顶点坐标,离心率和渐近线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee21768e63a701890f0b105797214a3.png)
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8 . 求与椭圆
共焦点且过点
的双曲线方程及其焦距,实轴长,虚轴长,渐近线方程,离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
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9 . 已知双曲线
,求双曲线的焦点坐标、离心率和渐近线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4cb2ebf5126d174b7a717abb853434.png)
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10 . 求适合下列条件的椭圆的标准方程.
(1)焦距为8,且椭圆上任一点到两焦点的距离之和为12;
(2)与双曲线
有相同的焦点,长轴长是10.
(1)焦距为8,且椭圆上任一点到两焦点的距离之和为12;
(2)与双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b0c45fac5e9dfc6ad50bd215ef28d4.png)
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