解题方法
1 . 已知
是双曲线
的右焦点,圆
与双曲线C的渐近线在第一象限交于点A,点B在双曲线C上,
,则双曲线C的渐近线方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b96eda0601673fafb836643969914f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76eca66a13eeabe79410c25eb56a630f.png)
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2 . 设
是面积为1的等腰直角三角形,D是斜边AB的中点,点P在
所在的平面内,记
与
的面积分别为
,
,且
.当
,且
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05c938fd42f5cb0b9d21cd44acbec6e.png)
________ ;记
,则实数a的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177678001b2ccde1db8f57fa5e017002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fa5b7ee3c02add5668fcdfd13e4b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779f538be94aff22b3eedabfc4c11be4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e81f85f2c7f054f32a01e17f4aa8fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51336413ab117b448511bdcd4758e39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05c938fd42f5cb0b9d21cd44acbec6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169436bf1e8baa899a0179a1c0409947.png)
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解题方法
3 . 已知
,
分别是双曲线C:
(
)的左、右焦点,过
作一直线交C于M,N两点,若
,且
的周长为1.则C的焦距为___________ .
![](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/99b343054b22bb3d30eeec12c3ae4d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f0ec66ed29f6a7d502a9da85ab2760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656690e5d6fe1b44a4983086229f34ae.png)
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解题方法
4 . 已知双曲线
:
,
是坐标原点,
,
分别是
的左、右焦点,点
是
上任意一点,过
作双曲线
渐近线的垂线,垂足为
,则
的长为________ ;过
作
角平分线的垂线,垂足为
,则
的长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c465114dc2665d74246240b1d4d26ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7272356beb98a7953a49651324cb6455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
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名校
解题方法
5 . 已知双曲线C:
(
,
)的左、右焦点分别为
,
,过点
的直线与C的右支交于A,B两点,且
,
的内切圆半径
,则C的离心率为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.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/d41b7fb0e1d060142072369c01cf0613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522a26b166434b4ffe911c471ed445c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f624de3b02e1096dd91a8a56f3eedcaf.png)
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2024-01-18更新
|
682次组卷
|
2卷引用:山东省济南市2024届高三上学期期末学习质量检测数学试题
名校
解题方法
6 . 已知双曲线
:
的左、右焦点分别为
,
,倾斜角为
的直线
与双曲线
在第一象限交于点
,若
,则双曲线
的离心率的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.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/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.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/b92247e1bcbc7c2678b18fc9375b2717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2023-12-28更新
|
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5卷引用:江苏省泰州市兴化市2024届高三上学期期末适应性考试数学试题
江苏省泰州市兴化市2024届高三上学期期末适应性考试数学试题2024届广东省部分学校高三12月联考一模数学试题江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(八)(已下线)模块5 周期变化篇 第5讲:三角形中的最值范围问题【练】宁夏回族自治区银川市银川一中2024届高三上学期第六次月考数学(理)试题
2023·全国·模拟预测
名校
解题方法
7 . 已知
,
分别为双曲线
的左、右焦点,过
的直线与双曲线左支交于A,B两点,且
,以
为圆心,
为半径的圆经过点
,则
的离心率为______ .
![](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/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac00c0db17b7bf34f758f73cd4c6a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d107e77106ff1a9cb76b504bbc99bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2023-12-24更新
|
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4卷引用:湖北省新洲区部分学校2024届高三上学期期末数学试题
湖北省新洲区部分学校2024届高三上学期期末数学试题(已下线)2024年全国高考名校名师联席命制型数学信息卷(四)(已下线)【一题多解】巧求离心率 坐标与几何上海市同济大学第一附属中学2023-2024学年高二下学期期中考试数学试题
名校
8 . 已知
,
是双曲线
的左、右焦点,点
在双曲线上,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e203545563ef6c33968cd9fab532638e.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/9c99580b2a33da8968f0f7f86b89492e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8a952a1380148042d4ef38e491a532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e203545563ef6c33968cd9fab532638e.png)
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2023-12-23更新
|
449次组卷
|
2卷引用:黑龙江省哈尔滨市第三中学校2023届高三上学期期末考试数学试题
名校
解题方法
9 . 已知双曲线
的左,右焦点分别为
,
,过左焦点
作直线
与双曲线交于A,B两点(B在第一象限),若线段
的中垂线经过点
,且点
到直线
的距离为
,则双曲线的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e24b2ff05ffec78200a3f8241aabf6.png)
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2023-12-22更新
|
1055次组卷
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6卷引用:上海市普陀区曹杨第二中学2024届高三上学期期末数学试题
名校
10 . 设椭圆
双曲线
共焦点
,
,离心率分别为
,
,其中
.设曲线
,
在第一、三象限的交点分别为点
,
,若四边形
为矩形,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ced3c956c7292540692adf70b41fd4.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99cd361ce118bca96a731b241a9c587d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7faba14550b7d88f14c29c0d6f0ff2.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/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd51098c53747262fa125f1a82781620.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bf783e77164a07adedb41ae0b3aaa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ced3c956c7292540692adf70b41fd4.png)
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2023-12-19更新
|
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4卷引用:山东省泰安市新泰中学2024届高三上学期期末仿真模拟数学试题