名校
解题方法
1 . 已知双曲线
的左、右焦点分别为
,根据双曲线的光学性质可知,过双曲线
上任意一点
的切线
平分
.直线
过
交双曲线
的右支于A,B两点,设
的内心分别为
,若
与
的面积之比为
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c29bab2a74ca02d30e0deed068b042f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bac2f7fe4411d15bdeb4a72e98ea766e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/6b1bd8fd746ffacd779249f171d80168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e1fcb61ab66a7f514b7bad31d1e2f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed517e1f28671f9dac3264ced2720a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e68113ebf789709f8a98d9e5f2f8a31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-11更新
|
574次组卷
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3卷引用:湖南省益阳市2024届高三下学期5月适应性考试数学试题
名校
解题方法
2 . 已知双曲线
(
,
)的左、右焦点分别为
、
,圆
与双曲线在第一象限和第三象限的交点分别为
,
,四边形
的周长
与面积
满足
,则该双曲线的离心率为( )
![](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/8608eba9de6c245cfa5e5ce6d436aa7e.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/bb0389adcd388a91d4b84d2dc87ccc65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8cee1103894119725ed04bdf9de1adf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-11-10更新
|
2978次组卷
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10卷引用:湖南省长沙市第一中学2020-2021学年高三上学期月考(三)数学试题
湖南省长沙市第一中学2020-2021学年高三上学期月考(三)数学试题(已下线)第九单元 解析几何 (A卷 基础过关检测)-2021年高考数学(理)一轮复习单元滚动双测卷(已下线)第九单元 解析几何 (A卷 基础过关检测)-2021年高考数学(文)一轮复习单元滚动双测卷江西省新余市第一中学2020-2021学年高二年级第六次考试数学(文)试题浙江省杭州第二中学2021届高三下学期3月开学考试数学试题辽宁省辽南协作校2020-2021学年高二上学期期末数学试题辽宁省抚顺二中、沈阳二中等2020-2021学年高二上学期期末考试数学试题重庆市主城区2021届高三上学期适应性(一)数学试题(已下线)第2章 圆锥曲线 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)云南省玉溪市第一中学2023-2024学年高二下学期3月月考数学试题
名校
解题方法
3 . 已知双曲线
的左、右焦点为
、
,虚轴长为
,离心率为
,过
的左焦点
作直线
交
的左支于A、B两点.
(1)求双曲线C的方程;
(2)若
,求
的大小;
(3)若
,试问:是否存在直线
,使得点
在以
为直径的圆上?请说明理由.
![](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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求双曲线C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c783d7c6ccce0eb16cb9985472c3d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62180fb2b68724b7b0f4f8337496c12a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accf35598ee054f1bf8b6584641d6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-01-15更新
|
567次组卷
|
4卷引用:湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题
湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题上海市川沙中学2023-2024学年高二上学期期末考试数学试卷江苏省南京市金陵中学2024届高三上学期期末模拟数学试题(已下线)第2章 圆锥曲线 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
4 . (多选)已知
是椭圆
(
)和双曲线
(
)的公共焦点,
是他们的一个公共点,且
,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64fbb01ca05af7aec2ff98b4d4fabb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e0ddeac5d77078e2453f9402b40553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894ee014d39c8d3f1d934e4d3dbba46e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250bd38b5bb4c9c06011ce6fd9f0729e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db634c178cd7bffbd4cb886e3f2cca22.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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2020-12-06更新
|
2686次组卷
|
8卷引用:湖南省常德市临澧县第一中学2020-2021学年高二上学期第三次阶段性考试数学试题
名校
解题方法
5 . 双曲线的第三定义是:到两条相交直线的距离之积是定值的点的轨迹是(两组)双曲线.人教A版必修第一册第92页上“探究与发现”的学习内容是“探究函数
的图象与性质”,经探究它的图象实际上是以两条坐标轴为渐近线的双曲线,进一步探究可以发现对勾函数
,
的图象是以直线
,
为渐近线的双曲线.现将函数
的图象绕原点顺时针旋转得到焦点位于
轴上的双曲线
,则它的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad123b73302cb4ea2d0a30bd912ec42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26d3f9d8344e1c727fbbed5421daaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1447dbe580ac5c825776995118e75acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91951332bd1ded2aae1246af6619df4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2024-01-13更新
|
571次组卷
|
2卷引用:湖南省常德市第一中学2024届高三上学期第六次月考数学试题
名校
解题方法
6 . 已知
,
分别是双曲线
,
的左、右焦点,双曲线上有一点
,满足
,且
,则该双曲线离心率的取值范围是____
![](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/a86d91f7014ffb9b8814758c1ac87c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04174f3c9351bc05bcf604d18ab8c44c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd461f264873547b2170408ea4ad9cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
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|
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|
6卷引用:湖南省长沙市第一中学2022-2023学年高二下学期期末数学试题
名校
解题方法
7 . 已知双曲线
的左右焦点分别为F1,F2,点M是双曲线右支上一点,满足
,点N是F1F2线段上一点,满足
.现将△MF1F2沿MN折成直二面角
,若使折叠后点F1,F2距离最小,则
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54099108fd9bbeed602a46ab32c9ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19de2aa3e4ebac2e720d6b3e04523847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63926bfe65495cd79e1140d4798158d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0447080451da5404ff47078587fb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-09-08更新
|
1749次组卷
|
5卷引用:湖南省邵阳市邵东市第一中学2021-2022学年高二下学期第一次月考数学试题
湖南省邵阳市邵东市第一中学2021-2022学年高二下学期第一次月考数学试题湖南省长沙市长郡中学2023届高三二模数学试题重庆市西南大学附属中学2022届高三上学期开学考试数学试题(已下线)考点34 二面角【理】-备战2022年高考数学典型试题解读与变式(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点6 圆锥曲线中的翻折问题(一)
8 . 已知双曲线
:
,
,
分别为双曲线的左、右焦点,
为双曲线上的第一象限内的点,点
为
的内心,
的面积的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c58fa4a337f0b81b991fb32e8e6e3c0.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/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4066a709cfc78a4d56145c9970b7b852.png)
您最近一年使用:0次
9 . 已知双曲线
:
过点
,且右焦点为
.
(1)求双曲线
的方程;
(2)过点
的直线
与双曲线
的右支交于
,
两点,交
轴于点
,若
,
,求证:
为定值.
(3)在(2)的条件下,若点
是点
关于原点
的对称点,求证:三角形
的面积
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a9c02ee8d3bf4f87bbda54a82672fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38480259a54626c1bf2d6973bcd38a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a444d2f0edc4a28a0ee195d7caf06277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
(3)在(2)的条件下,若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c606f78391198b6648ba0b92b60f8cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/119efeb12f67c9507a77fc7a3089523c.png)
您最近一年使用:0次
2023-03-20更新
|
400次组卷
|
2卷引用:湖南省益阳市南县第一中学2023-2024学年高二上学期期末模拟数学试题
名校
解题方法
10 . 已知
,
分别是双曲线
的左、右焦点,点
为坐标原点,过
的直线分别交双曲线左、右两支于
,
两点,点
在
轴上,
,
平分
,其中一条渐近线与线段
交于点
,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/578832b5e2b61bf599918028e68da17f.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/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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad0573a91986064275b3beaa3749e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0efe810673fd4ca71c659e01197942.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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