名校
解题方法
1 . 如图,已知双曲线
的左右焦点分别为
、
,
,
是双曲线右支上的一点,
,直线
与
轴交于点
,
的内切圆半径为
,则双曲线的离心率是( )
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897622194544640/2904076407955456/STEM/0a10d24b-9f10-4c15-b2c6-f07064832f2c.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/404e44d752d3efae82797f009d2c0ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa65e9e7125c4bd360cf71ea4439e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897622194544640/2904076407955456/STEM/0a10d24b-9f10-4c15-b2c6-f07064832f2c.png?resizew=165)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4卷引用:湖南省张家界市2021-2022学年高二上学期期末联考数学试题
名校
2 . 如图,
是椭圆
与双曲线
在第一象限的交点,且
共焦点
的离心率分别为
,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898463835054080/2903041919180800/STEM/0a33b1f2-b8f2-4f92-8ee8-adb292670fc9.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d101bd6b9e4d8bda938e85d2ddce2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e7ebc3957605253abb7546bea0323f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f994a876391534efe497dc115a53e3fa.png)
![](https://img.xkw.com/dksih/QBM/2022/1/20/2898463835054080/2903041919180800/STEM/0a33b1f2-b8f2-4f92-8ee8-adb292670fc9.png?resizew=167)
A.![]() | B.若![]() ![]() |
C.若![]() ![]() | D.![]() |
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7卷引用:湖北省2021-2022学年高二上学期期末调考数学试题
湖北省2021-2022学年高二上学期期末调考数学试题广东省广州市第九十七中学2022-2023学年高二上学期期末数学试题(已下线)专题17 椭圆与双曲线共焦点问题 微点3 椭圆与双曲线共焦点常用结论及其应用(三)江苏省南京市金陵中学2023-2024学年高二上学期10月月考数学试题(已下线)重难点突破04 轻松搞定圆锥曲线离心率十九大模型(十九大题型)-2湖北省鄂州市第二中学2023-2024学年高二上学期12月月考数学试题(已下线)微考点6-4 利用二级结论秒杀椭圆双曲线中的选填题
3 . 已知
,
分别是椭圆
和双曲线
的离心率,
,
是它们的公共焦点,M是它们的一个公共点,且
,则
的最大值为______ .
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/74404619ad5699e6c44c947fb569600f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2770478f4c5e9339f84a0c39c66a4e59.png)
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2卷引用:湖北省襄阳市2021-2022学年高二上学期元月期末数学试题
解题方法
4 . 如图所示,已知
分别为双曲线
的左、右焦点,过
的直线与双曲线的右支交于
两点,记
的内切圆
的面积为
,
的内切圆
的面积为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/1/f1249fb2-1e91-4039-9106-af2f5ff90911.png?resizew=208)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c477e5ade921ffa8377c4719319380ff.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/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/1/f1249fb2-1e91-4039-9106-af2f5ff90911.png?resizew=208)
A.圆![]() ![]() | B.圆心![]() ![]() |
C.![]() | D.![]() ![]() |
您最近一年使用:0次
2022-01-26更新
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1584次组卷
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2卷引用:浙江省绍兴市诸暨市2021-2022学年高二上学期期末数学试题
名校
解题方法
5 . 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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6卷引用:浙江省丽水市2021-2022学年高二上学期期末教学质量监控数学试题
名校
6 . 已知双曲线
的左,右焦点分别为
,
,过右焦点
且倾斜角为
直线l与该双曲线交于M,N两点(点M位于第一象限),
的内切圆半径为
,
的内切圆半径为
,则
为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1653c086d557b1845d82c2d4d8231f8.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc18a5bb2e53586331b2a58538a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12bdb8e9f4bd99efe2c4cdb7234b1298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e34cb2921334b3a4bc856eed3a825d2.png)
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7卷引用:广东省东莞市2021-2022学年高二上学期期末数学试题
广东省东莞市2021-2022学年高二上学期期末数学试题江西省赣州市赣县第三中学2021-2022学年高二4月月考数学(理)试题(已下线)专题08 平面解析几何(文理)辽宁省沈阳市东北育才学校2022-2023学年高三下学期高考适应性测试(三)数学试题安徽省江南十校2022-2023学年高二下学期5月联考数学模拟试题(已下线)3.2.2 双曲线的简单的几何性质(重难点突破)-【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)海南省部分学校2024届新高考二卷押题卷(三)数学试题
名校
7 . 已知椭圆和双曲线有相同的焦点
和
,设椭圆和双曲线的离心率分别为
,
,
为两曲线的一个公共点,且
(
为坐标原点).若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da56e20ed2432083fe264ed9624f71f5.png)
,则
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/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e302585cf470349c74cacadd31c25e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da56e20ed2432083fe264ed9624f71f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ceced01c56a129eb22aa300d1b4f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
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|
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9卷引用:四川省成都市2021-2022学年高二上学期期末考文科数学试题
四川省成都市2021-2022学年高二上学期期末考文科数学试题四川省成都市2021-2022学年高二上学期期末考试理科数学试题广西南宁市宾阳县宾阳中学2021-2022学年高二上学期期末考试数学(理)试题山东省淄博实验中学2021-2022学年高二下学期开学考试数学试题(已下线)必刷卷02(理)-2022年高考数学考前信息必刷卷(全国甲卷)四川省成都经济技术开发区实验中学校2022-2023学年高二上学期期末考试数学(文)试题(已下线)专题 3.3 双曲线性质归类(3)(已下线)第10题 共焦点的椭圆离心率问题(压轴小题)(已下线)模型10 向量与解析几何问题模型
8 . 已知F是双曲线
的右焦点,若直线
与双曲线相交于A,B两点,且
,则k的范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae5dfec6fa25fe7ddc417c11115d768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/185ebcb889a4731b1c28ef0116f4a461.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知
,
,
为平面上一动点,且满足
,记动点
的轨迹为曲线
.
(1)求曲线
的方程.
(2)若
,
过点
的动直线
:
交曲线
于
,
(不同于
,
)两点,直线
与直线
斜率分别记为
,
.
①求
的范围.
②证明:
为定值,并计算定值的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eda2eac3ad21518f181b966edc7c81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b74230f604916c843cfeeb0fe19501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2fc44c5dfd20e5e1c74b251b61457c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dcfafc42b4dfe71c68ca3b736eea1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715b8ed88611ca407427147537a589e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/f9153ab748ff66af41e5f56b12f327cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0684655e622ec9677660a79a013754f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6ae9d26b2f1d297dfd9f12af57ddea.png)
您最近一年使用:0次
2022-01-13更新
|
731次组卷
|
4卷引用:浙江省金华十校2022-2023学年高二上学期期末联考模拟数学试题1
浙江省金华十校2022-2023学年高二上学期期末联考模拟数学试题1(已下线)数学-2022届高三下学期开学摸底考试卷(江苏专用)江苏省盐城市四校2022届高三下学期期初联合检测数学试题重庆市育才中学2021-2022学年高二上学期期中数学试题
名校
解题方法
10 . 已知动圆
过点
,并且与圆
外切,设动圆的圆心
的轨迹为
.
(1)求曲线
的方程;
(2)过动点
作直线与曲线
交于
,
两点,当
为
的中点时,求
的值;
(3)过点
的直线
与曲线
交于
,
两点,设直线
,点
,直线
交
于点
,证明直线
经过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c2124260496e9307d6448c0c943f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69b0d917d1c2635fadb820329ab4390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8961be6a63ff90a1404772abcb435bb.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b91607dd83520860a563433617664d0.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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4卷引用:浙江省金华十校2022-2023学年高二上学期期末联考模拟数学试题2
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