1 . 设双曲线
:
的左、右焦点分别为
,
,
为双曲线
上一点,
关于原点的对称点为
,若四边形
面积为
,则这个四边形的周长为______ .
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27567d43c5b91382ee3d7ca708ee422.png)
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2 . 设点
,
是正三角形,且点
在双曲线
上,点
关于____ 对称,
的周长是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0310ce4692c85c9702f564923a55f98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf44d5bde76c29c3a6508f0523d3615.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
3 . 已知
,
分别为双曲线C:
(
,
)的左、右焦点,O为坐标原点.若右支上一点P满足
,且
,则C的渐近线方程为______ .
![](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/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/4d8d042c651b485fcb08c765bea3e292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be23728dc83a1a6d3ef27a797b2dc77e.png)
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名校
4 . 过原点的直线
与双曲线
的左右两支分别相交于A、B两点,
是双曲线的左焦点,若
,
,则双曲线的方程是_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c37b8fcd4765dd6c35bf246377b28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61e0d231313504ccd89a9f3b0cab78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d8ae2e6458bc87b823da97e0cb1f6a.png)
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2020-02-10更新
|
185次组卷
|
2卷引用:上海市上海交大附中2016-2017学年高二上学期12月月考数学试题
名校
5 . 双曲线
绕坐标原点
旋转适当角度可以成为函数
的图象,关于此函数
有如下四个命题:①
是奇函数;②
的图象过点
或
;③
的值域是
;④ 函数
有两个零点;则其中所有真命题的序号为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e409849c921f4868c5a78abffb9f74bb.png)
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2020-01-16更新
|
548次组卷
|
6卷引用:上海市奉城高级中学2019-2020学年高二上学期期末数学试题
上海市奉城高级中学2019-2020学年高二上学期期末数学试题上海市格致中学2022-2023学年高二下学期第二次测试数学试题2018年上海市普陀区高三一模数学试题(已下线)重难点06 解析几何-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)课时37 双曲线-2022年高考数学一轮复习小题多维练(上海专用)(已下线)专题19 圆锥曲线 (模拟练)-1
名校
6 . 若三个点
,
,
中恰有两个点在双曲线
:
上,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4157726dc056734b4e611f26f4e22c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567b8b78cb08fbc5aa00e81c5e7e547e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe3a946404ef2f045737c440e8817ed.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2020-01-12更新
|
421次组卷
|
6卷引用:湖南省湖南师范大学附属中学2019-2020学年高二上学期期中考试 数学
7 . 已知双曲线
:
的右焦点为
,以
为圆心,以
为半径的圆交双曲线
的右支于
,
两点(
为坐标原点),
的一个内角为
,则双曲线
的离心率为_______ .
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8b3616d8d33f54ddac1c485a95a7cf.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/acc290b44635265137fdf13146b6a6d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2019-05-12更新
|
1421次组卷
|
4卷引用:重庆市缙云教育联盟2021-2022学年高二上学期9月月度质量检测数学试题
重庆市缙云教育联盟2021-2022学年高二上学期9月月度质量检测数学试题【市级联考】山东省济宁市2019届5月高考模拟考试(二模)理科数学试题(已下线)专题28 双曲线-冲刺2020高考跳出题海之高三数学模拟试题精中选萃吉林省长春市北师大附属学校2021-2022学年高三上学期期初考试数学(理)试题
名校
8 . 已知双曲线
的右焦点为
,过原点的直线与双曲线
相交于
两点,连接
,若
,
,
,则该双曲线的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660964e4c6710e01ba34521ad419c3ae.png)
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2019-01-20更新
|
785次组卷
|
6卷引用:【市级联考】辽宁省大连市2018-2019学年高二上学期期末考试数学(理)试题
名校
9 . 已知双曲线C的方程为
,过原点O的直线l与双曲线C相交于A、B两点,点F为双曲线C的左焦点,且
,则
的面积为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51c50e43436e0b72975bc4a69f8cffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecfced297fe0bdd35926c0eeff8f65d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afac6934256a23613443c393446881a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/62a3b585-f22d-427d-8277-3516d675f304.png?resizew=166)
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2019-01-02更新
|
1001次组卷
|
6卷引用:四川省蓉城名校联盟高2017级高二上期12月月考文科数学试题
四川省蓉城名校联盟高2017级高二上期12月月考文科数学试题【校级联考】四川省蓉城名校联盟2018-2019学年高二上学期期末联考数学(文)试题四川省新津中学2019-2020学年高二4月月考(入学)数学试题(已下线)第三章 圆锥曲线与方程(能力提升)-2020-2021学年高二数学单元测试定心卷(北师大版选修2-1)人教A版(2019) 选修第一册 数学奇书 第三章 学业评价(三十一)人教A版(2019) 选修第一册 数学奇书 第三章 圆锥曲线的方程 3.2.2 双曲线的简单几何性质 第2课时 双曲线方程与性质的应用
2018高二上·全国·专题练习
10 . 设
分别是双曲线
:
的左、右焦点,过点
且垂直于
轴的直线与双曲线
交于
两点,若点
满足
,则双曲线的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9b19dfc40f5ac92d489480c488a211.png)
________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a1aa3ff557146cf50fb2240e2f1389f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9b19dfc40f5ac92d489480c488a211.png)
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