名校
解题方法
1 . (多选)已知
是一个等腰直角三角形,如果圆锥曲线以
的两个顶点为焦点,且经过另外一个顶点,则该圆锥曲线的离心率可以等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-09-27更新
|
453次组卷
|
2卷引用:人教B版(2019) 选择性必修第一册 过关斩将 第二章 平面解析几何 本章复习提升
名校
解题方法
2 . 已知
,
是双曲线
的两个焦点,点
是双曲线的右顶点,
是双曲线渐近线上一点,满足
,若以
为焦点的抛物线
经过点
,则此双曲线的离心率为
![](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/ebe294e939b9fb81256d7218a773b5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef54c426564ae8fc43cbfd92b6fb534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf1590b0b3d72cacdc37cb7c213a023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() | C.2 | D.![]() |
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2020-03-23更新
|
442次组卷
|
7卷引用:【市级联考】吉林省延边州2019届高三2月复习质量检测数学(理)试题
解题方法
3 . 已知
,
是双曲线
,
的两个焦点,以线段
为边作正三角形
,若边
的中点在双曲线上,则双曲线的离心率是( )
![](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/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f311053d11884b1a21d5f9b5724996c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a6919a10602b63c55a9bb6fee29c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b67528f875a6d4bac8bbf784f7b66a0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-05-15更新
|
413次组卷
|
3卷引用:2020届吉林省延边州高三下学期4月教学质量检测数学(理)试题
名校
解题方法
4 . 过双曲线
(
,
)的右焦点
作倾斜角为
的直线
,和双曲线在第一象限交于点
,
是等腰三角形(
为坐标原点),则双曲线的离心率为( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e55b85a1dc91ee8a026ad44e82d42b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.2 | B.![]() | C.![]() | D.![]() |
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2020-10-20更新
|
417次组卷
|
2卷引用:吉林省梅河口市第五中学2020届高三第七次模拟考试数学(理)试题
名校
5 . 已知双曲线
的渐近线被圆
截得的弦长为
,则该双曲线的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ecf7240772bb21d8ed901c3077e35d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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2017-05-11更新
|
1341次组卷
|
9卷引用:吉林省东北师范大学附属中学2017届高三下学期第三次模拟考试数学(文)试题
6 . 已知
,
是双曲线
(
>0,
>0)的两个焦点,
是经过
且垂直于
轴的双曲线的弦,若
=
,则双曲线的离心率是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5b0b2c0a3223b2045569567900fc05.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5b0b2c0a3223b2045569567900fc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8468ada1f9ae26172046b278e987fe75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1508f3ca7797b21ee388b56410103c95.png)
A.2 | B.![]() | C.![]() | D.![]() ![]() |
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7 . 过双曲线
=" 1" (a > 0,b > 0)的一个焦点F向其一条渐近线作垂线
, 垂足为A,
与
另一条渐近线交于B点, 若
, 则双曲线的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a626eed1d14c35d285b1b97a21ced33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
另一条渐近线交于B点, 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc81ab05c3c8889f1460d33e0baa63e6.png)
A.2 | B.![]() | C.![]() | D.![]() |
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2017-03-15更新
|
769次组卷
|
10卷引用:2012届江西省宜春市高三模拟考试理科数学试卷
(已下线)2012届江西省宜春市高三模拟考试理科数学试卷2015届重庆市巴蜀中学高三上学期第一次模拟考试理科数学试卷2015届辽宁省锦州市高三质量检测二理科数学试卷2015届辽宁省锦州市高三质量检测二文科数学试卷2016届湖南长沙长郡中学高三下学期第六次月考文科数学试卷2016-2017学年山东省胶州市普通高中高二上学期期末考试数学(文)试卷2016-2017学年山东省胶州市普通高中高二上学期期末考试文数试卷广州市岭南中学2017学年第一学期高三年级期中考试理科数学试题广东省广州六中2019-2020学年高二下学期期末数学(理)试题吉林省实验中学2021-2022学年高三上学期第二次学科诊断测试理科数学试题
名校
8 . 已知双曲线
的离心率为
.
(1)求双曲线
的方程.
(2)直线
与该双曲线
交于不同的两点
、
,且
、
两点都在以点
为圆心的同一圆上,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ce1534a372db7666711443631c4ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3753245424ff38023cd4ef5d6ab533.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6cffa52177f31cd10c42d00f69d4da1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2019-01-10更新
|
458次组卷
|
3卷引用:【市级联考】吉林省长春市榆树一中五校2018-2019学年高二上学期期末联考数学(文)试题
解题方法
9 . 已知双曲线
(
)的左、右焦点分别为
,
是双曲线
上的两点,且
,
,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4129b3e1222eccec28034e113fa4c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1210aed3ea71f3429901679dfbdb40af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f0da59665ee656a3781f9c485ef8d1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2018-03-29更新
|
1051次组卷
|
4卷引用:【校级联考】吉林省五地六校2018-2019学年高三(上)期末数学试题
名校
10 . 已知
,
是椭圆
与双曲线
共同的焦点,椭圆的一个短轴端点为
,直线
与双曲线的一条渐近线平行,椭圆
与双曲线
的离心率分别为
,
,则
取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b283e4d7375d770823775e4036c9f6d0.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/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ed6e21185ce4b8eadc7c807806bde5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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