名校
1 . 已知双曲线
的左、右焦点分别为
,
,以
为直径的圆与双曲线的四个交点依次连线恰好构成一个正方形,则双曲线的离心率为.
![](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/643ef7d761de0e794fc39937dc72ac6a.png)
A.![]() | B.![]() | C.2 | D.![]() |
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2020-01-06更新
|
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名校
2 . 已知椭圆、双曲线均是以线段
的两端点为焦点的曲线,点B是它们的一个公共点且满足
,记此椭圆和双曲线的离心率分别为
、
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d95ea30a3550d19b7ac912ae3fe0900.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/51663ae7f8163e23c959ead7b2e0a127.png)
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3 . 已知双曲线
的右顶点为
,以
为圆心,
为半径作圆
,圆
与双曲线
的一条渐近线交于
、
两点,若
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0d90b0b275bc85b16a918a3dc697fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec4bcdebd233b3c6c352a85c7fe3f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知双曲线
过点
且渐近线为
,则下列结论正确的个数为( )
①
的实轴长为
;②
的离心率为
;
③曲线
经过
的一个焦点;④直线
与
有两个公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460e1f707e43e4d7a8a2eb6bfaa435e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b75308335340230171130238f4dc6c1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b775a6d895e62f08ec02842ace63565d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b835e357470ee8513c579054921bf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知双曲线
的右焦点为
,直线
与
交于
、
两点,
、
的中点分别为
、
,若以线段
为直径的圆经过原点,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a0d90b0b275bc85b16a918a3dc697fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e04a6d711600fc4f8a8df876a85cce.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/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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2019年11月中学生标准学术能力诊断性测试测试文科数学试题(一卷)河南省顶级名校2019-2020学年高三尖子生11月诊断性检测数学(文)试卷(已下线)河北省石家庄精英中学2023届高三上学期第三次调研数学试题
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6 . 过双曲线
的右焦点
作一条渐近线的垂线,与
左支交于点
,若
,则
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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354a4197bf41b6dfcb53544afcb6af68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.2 | C.![]() | D.5 |
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|
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名校
7 . 已知双曲线
的焦点到渐近线的距离为
,且离心率为
,则该双曲线的实轴的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 设
、
分别为双曲线
的左、右顶点,
、
是双曲线
上关于
轴对称的不同两点,设直线
、
的斜率分别为
、
,若
,则双曲线
的离心率
是( )
![](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/6a0d90b0b275bc85b16a918a3dc697fc.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbb20cf7da78670140c60578ce7d82cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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名校
9 . 已知点
,
分别是双曲线
的左、右焦点,过
且垂直于x轴的直线与双曲线交于A,B两点,若
是锐角三角形,则双曲线离心率的范围是( )
![](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/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/635a0150fe965ced8935d7479b22c508.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:陕西省汉中市十校2022届高三下学期第二次联考文科数学试题
陕西省汉中市十校2022届高三下学期第二次联考文科数学试题黑龙江省鹤岗市第一中学2019-2020学年高二上学期期中数学(理)试题浙江省嘉兴八校联盟2021-2022学年高二上学期期中联考数学试题山东省潍坊市昌乐二中2023-2024学年高二上学期期末拉练数学试题(二)(已下线)专题19 双曲线离心率定值及取值范围(期末选择题19)-2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)
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10 . 已知双曲线
:
(
,
)的左、右顶点分别为
,
,左焦点为
,
为
上一点,且
轴,过点
的直线
与线段
交于点
,与
轴交于点
,直线
与
轴交于点
,若
(
为坐标原点),则
的离心率为
![](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/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.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/a0ed1ec316bc54c37c4286c208f55667.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/08b1da9046b4cb82135a4a1eaa528c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665a9488b39cd5070b138db6530c1e54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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云南省师范大学附属中学2019-2020学年高三上学期11月月考数学(文)试题2020届云南师范大学附属中学高三适应性月考卷(三)数学文科试题2020届云南师范大学附属中学高三上学期第三次月考数学(理)试题江苏省南通市平潮高中2020-2021学年高三上学期11月学情检测数学试题云南省师范大学附属中学2019-2020学年高三上学期11月月考数学(理)试题山西省运城市康杰中学2018届高考模拟(一)数学(理)试题山西省运城市康杰中学2018届高三高考模拟(一)数学(文)试题【市级联考】山东省日照市2017届高三下学期第一次模拟考试数学(理)试题【全国百强校】安徽省六安市第一中学2019届高三下学期高考模拟考试(三)数学(文)试题四川省成都市棠湖中学2018-2019学年高二下学期期末考试数学(文)试题四川省泸州市泸县第五中学2019-2020学年高三上学期期末考试数学(理)试题