1 . 设双曲线
的左、右焦点分别为
,点P在C的右支上,当
时,
_______ ;当P运动时,
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b71f578f9716fd213e262d06ed413b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0d15c0cd066349600c876371580863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda59d9787314cc9ae5b122a4847e24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455b2aed42d9a79dd7324ebd3ac46981.png)
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2 . 已知两点
.点
满足
,则
的面积是____ ;
的一个取值为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/398f352cf420a5d215e9dbd59eb85e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285f34134c43ba75b616c6591afa79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ece6688ab0291e339059af91e18cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2023-05-09更新
|
1115次组卷
|
4卷引用:北京市西城区2023届高三二模数学试题
北京市西城区2023届高三二模数学试题北京市第五十五中学2023-2024学年高三下学期三模数学试题北京市陈经纶中学2023-2024学年高二上学期期中考试数学试卷(已下线)第03讲 3.2.1双曲线及其标准方程(2)
名校
解题方法
3 . 设双曲线
的两个焦点为
、
,点
是圆
与双曲线
的一个公共点,
,则该双曲线的离心率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d12fbb4f6f052a3cfacee42a4b719ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d124b231bf2cd3746f35e6c68cd7178f.png)
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2023-04-08更新
|
1238次组卷
|
3卷引用:北京市中国人民大学附属中学2023届高三统练(4)数学试题
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解题方法
4 . 已知椭圆
和双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf1bce17440e83c1b735d2954010a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
有相同的焦点
,
,点
是
和
的一个交点.若点
满足
是正三角形且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654e60a0749ca2875a6aad49c3a0ee42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf1bce17440e83c1b735d2954010a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f311053d11884b1a21d5f9b5724996c6.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/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6380c54a58ed53ebe8977402b42c960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b511bf6ea77c0489bdc63a1174be0400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
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2023-01-03更新
|
718次组卷
|
3卷引用:北京市2023届高三“极光杯”跨年线上测试数学试题
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解题方法
5 . 已知点
.若曲线
上存在两点
,使
为正三角形,则称
为
型曲线.给定下列三条曲线:
①
;
②
;
③
.
其中,是
型曲线的有___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc9aa334c8a364cbc597127d60b2b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2b74eb226474d2253bf4cab617b1162.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6190da0e5748928b84d509ab832ef9cb.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bdabcb41ed25b34822be2cb0536239.png)
其中,是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
您最近一年使用:0次
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6 . 已知双曲线
左右焦点分别为
,过点
作与一条渐近线垂直的直线l,且l与双曲线的左右两支分别交于M,N两点,若
,则该双曲线的渐近线方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528a243eb93f63c1e126409be1fb3fb5.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/859c116c6d7695fd354a6d6df63c6800.png)
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2023-02-07更新
|
573次组卷
|
3卷引用:2021年清华大学文科营暨工科营(冬令营)数学试题
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解题方法
7 . 已知双曲线
的焦点为
,过
的直线与双曲线
的右支交于
两点.若
是公比为2的等比数列,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc20249c715edfc770c82c2a59be639b.png)
__________ .
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/4754dce8d23950a26ca4aec2a659e964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc20249c715edfc770c82c2a59be639b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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8 . 已知双曲线
的左、右焦点分别为
、
,直线
过双曲线
的一个焦点,并且与双曲线
的一条渐近线平行,则双曲线
的方程为________ ;若点
,则
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.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/0cc662d67a893788cd7afb77859414d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5f1d92f93f78420c3b867e728035da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cca0078dac072087b4fc30c2de4870.png)
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9 . 设双曲线
的两个焦点是
,点
在双曲线上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10a1524ae7b5ea94390df629782830c.png)
___________ ;若
为锐角,则点
的纵坐标的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e8dc11154dc4db67706addd24453e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10a1524ae7b5ea94390df629782830c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2022-01-14更新
|
926次组卷
|
3卷引用:北京市一零一中学2022届高三下学期三模数学试题
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解题方法
10 . 双曲线
的右焦点为
,点
的坐标为
,点
为双曲线左支上的动点,且
周长的最小值为8,则双曲线的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1b29a97a7f0c7975061381c7809874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa65e9e7125c4bd360cf71ea4439e2c.png)
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