名校
解题方法
1 . 设双曲线
的右焦点为
,点
为坐标原点,过点
的直线
与
的右支相交于
两点.
(1)当直线
与
轴垂直时,
,求
的离心率;
(2)当
的焦距为2时,
恒为锐角,求
的实轴长的取值范围.
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
(1)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2023-11-17更新
|
391次组卷
|
7卷引用:湖南师范大学附属中学2024届高三上学期摸底考试数学试题
湖南师范大学附属中学2024届高三上学期摸底考试数学试题浙江省杭州第二中学2023-2024学年高三上学期第一次月考数学试题 (已下线)专题1 解析几何与平面向量(已下线)考点14 直线与圆锥曲线相交问题 2024届高考数学考点总动员【练】江苏省南通市如皋中学2023-2024学年高三上学期数学阶段考试(二)(已下线)专题15 圆锥曲线综合(已下线)2.6.2 双曲线的几何性质(分层练习)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第一册)
名校
解题方法
2 . 已知
、
是双曲线
的左、右焦点,以
为圆心,
为半径的圆与
的一条渐近线切于点
,过
的直线
与
交于
、
两个不同的点,若
的离心率
,则下列结论中正确的序号有_____________ .
①
;
②
的最小值为
;
③若
,则
;
④若
、
同在
的左支上,则直线
的斜率
.
![](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/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.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/f5076289823db419f94e9c0c8f4aafd9.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6bb22548794223f3caef1016c7b8f1.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb8e4633ac2ba6064c7c1d37e14cb09.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031661aa4b14c3b9954ec444ad5b6f05.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39640d6179eb537de7f30b120c2a35d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89de99eec69785123d702c6a6b665db5.png)
④若
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cf5eaa68bfa7bb3ea3fddf6102482c.png)
您最近一年使用:0次
名校
解题方法
3 . 已知双曲线
的左、右焦点分别为
,过
作一条直线与双曲线右支交于
两点,坐标原点为
,若
,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/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b801b1a15a0709c7af409e62ddf5bce.png)
您最近一年使用:0次
2023-10-18更新
|
1491次组卷
|
5卷引用:湖南省长沙市长郡中学2024届高三上学期月考(四)数学试题
名校
解题方法
4 . 已知双曲线
的左、右焦点分别为
,过双曲线
上一点
向
轴作垂线,垂足为
,若
且
与
垂直,则双曲线
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df353cfa5078216d3916201e963012c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16c755ab3fea6ca99b13193a5d7e485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2023-10-05更新
|
1590次组卷
|
6卷引用:湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题
湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题吉林省长春市长春外国语学校2023-2024学年高三上学期期中数学试题福建省福州第八中学2024届高三上学期期中考试数学试题(已下线)湖南省邵阳市邵东创新实验学校2023-2024学年高二上学期期中数学试题(已下线)湖南省长沙市长郡中学2024届高三上学期月考(二)数学试题变式题15-18(已下线)3.2.2 双曲线的简单的几何性质(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
名校
解题方法
5 . (多选)已知点
,
是双曲线
:
的左、右焦点,
是双曲线
位于第一象限内一点,若
,
,则下列结论正确的是( )
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.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/2ce67f2138e7295cd72d66b2908cb6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bd64915ac29ea6acd490f547ba68a8.png)
A.![]() ![]() |
B.双曲线![]() ![]() |
C.双曲线![]() ![]() |
D.若双曲线![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 抛物线
的焦点到双曲线
的渐近线的距离是
,则该双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ea50968c62cd8df1b01d852086d261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ec7fa23be9cbe9a50607ea6bc8a4ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
A.![]() | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
2023-08-20更新
|
601次组卷
|
5卷引用:湖南省长沙市第一中学2023-2024学年高三上学期月考(一)数学试题
湖南省长沙市第一中学2023-2024学年高三上学期月考(一)数学试题(已下线)考点12 圆锥曲线的几何性质(椭圆,双曲线,抛物线) 2024届高考数学考点总动员【练】安徽省蚌埠市铁路中学2023-2024学年高二上学期期中检测数学试题河南省济源市2023-2024学年高二上学期期末质量调研数学试题江西省南昌市第十九中学2023-2024学年高二上学期期中考试数学试卷
名校
解题方法
7 . 已知直线
与圆
相切于点
,直线
与双曲线
的两条渐近线分别相交于
两点,且
为
的中点,则双曲线
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55ca8f88be8bb4ef9474d028bef9615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced50b45f2b649ecb3c565198ee5a9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64acf2cf103416ef9fdfbd01933f39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
名校
解题方法
8 . 对于椭圆:
,我们称双曲线:
为其伴随双曲线.已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
(
),它的离心率是其伴随双曲线
离心率的
倍.
伴随双曲线
的方程;
(2)如图,点
,
分别为
的下顶点和上焦点,过
的直线
与
上支交于
,
两点,设
的面积为
,
(其中
为坐标原点).若
的面积为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b26461529321c5e669bdf3c489c5d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf94b793fc211b45616da1d0b3335b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eac95d4bdf7fa0ad635dbd96f72b20f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)如图,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](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/4bcd8ee2d8367c167d6ae0abc741b6b8.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/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb7e00f8bacce4d649b535449f04568c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bee180aecbd9e8f22162d5757dfeea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bb7149659e99f611509be0f3b7d0e8.png)
您最近一年使用:0次
2023-08-10更新
|
1255次组卷
|
9卷引用:湖南省长沙市长郡中学2024届高三上学期月考(三)数学试题
名校
解题方法
9 . 已知点
为双曲线
的渐近线和抛物线
的一个公共点,若
到抛物线焦点的距离为5,则双曲线的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.2 |
您最近一年使用:0次
2023-06-14更新
|
346次组卷
|
3卷引用:湖南省长沙市明德中学2023-2024学年高三上学期入学考试数学试题
湖南省长沙市明德中学2023-2024学年高三上学期入学考试数学试题河北正定中学2022-2023学年高二下学期月考三数学试题(已下线)3.3.2 抛物线的简单的几何性质(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)
名校
解题方法
10 . 如图,椭圆的中心在原点,长轴
在x轴上.以
、
为焦点的双曲线交椭圆于C、D、
、
四点,且
.椭圆的一条弦AC交双曲线于E,设
,当
时,双曲线的离心率的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556fcd1212f948856209c4cc065a30b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dcc5064c2b69b3f362acd729036d95c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd30704a29aa12aee831adea646e03f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/31c835b0-6c37-4195-b178-971769edc8f2.png?resizew=175)
您最近一年使用:0次
2023-06-08更新
|
1017次组卷
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