名校
解题方法
1 . 已知点
分别为椭圆
的左、右焦点,
是坐标原点,点
在椭圆上,
是面积为
的等边三角形,则
的值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1a97cb6c3005e46c333129959c89fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881309775c3b6a9f4ed408838666342.png)
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3卷引用:上海市格致中学2020-2021学年高二上学期12月月考数学试题
名校
解题方法
2 . 如图,
为坐标原点,双曲线
和椭圆
均过点
,且以
的两个顶点和
的两个焦点为顶点的四边形面积为
的正方形.
的方程;
(2)是否存在直线
,使得
与
交于
两点,与
只有一个公共点,且
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cadb6f88905d3f9f5847bcab281863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7676dadad7feee027cf6067c7ad26fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25040a22387f7a45dd2879b9f9e7a39c.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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b8a61c4b5b4ba267d02c0da6f953e7.png)
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3 .
是过椭圆
右焦点
的弦,则弦长
的最小值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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4 . 已知椭圆
(常数
)的左顶点为
,点
,
为坐标原点.
(1)若
是椭圆
上任意一点,
,求
的值;
(2)若
是椭圆
上任意一点,
,求
的取值范围;
(3)设
是椭圆
上的两个动点,满足
,试探究
的面积是否为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3044df061f3c9b06e525722cca969a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06046947fc7737b7159e968065d0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385495ec3ecd33e95b9b671ccc2866b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c918ca5d4e6d46ed130f85e5fa608d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ab4019fb59a5d6bfb7d210c4637466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fdf1d541630bd7c2973fc327514e43.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7d5b7a335fb30a034976287aee9e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392d00243d81bf17ff3be81e7a7ee05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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3卷引用:上海市行知中学2020-2021学年高二上学期12月月考数学试题
名校
解题方法
5 . 已知双曲线
的方程为
.
(1)直线
与双曲线的一支有两个不同的交点,求
的取值范围;
(2)过双曲线
上一点
的直线分别交两条渐近线于
两点,且
是线段
的中点,求证:
为常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a44342c2ee26a279265225982499b71.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19154d71383328a57153a293beb1faec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)过双曲线
![](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/8e3a1467ecf286e3cadaf5aa006606f2.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/28b6ab702f8e93cc1e680a7d7af06786.png)
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3卷引用:上海市行知中学2020-2021学年高二上学期12月月考数学试题
上海市行知中学2020-2021学年高二上学期12月月考数学试题湖北省襄阳市老河口市第一中学2022-2023学年高二上学期元月月考数学试题(已下线)广东省深圳市高级中学(集团)2023届高三上学期期末数学试题变式题17-22
6 . 已知曲线
,过点
作直线
和曲线
交于A、B两点.
(1)求曲线
的焦点到它的渐近线之间的距离;
(2)若
,点
在第一象限,
轴,垂足为
,连结
,求直线
倾斜角的取值范围;
(3)过点
作另一条直线
,
和曲线
交于
、
两点,问是否存在实数
,使得
和
同时成立?如果存在,求出满足条件的实数
的取值集合,如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4058fc45c49e6710ba7e273cb7888704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439e95540157803d4ac3cf61a49f50a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7277dcfb480720f2f37413cb0d34d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020c41eb2060b190e9cc01555016f533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a795a705795fe47cf57c4313b7b5d688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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3卷引用:上海市浦东新区2019-2020学年高三上学期期末数学试题
名校
7 . 已知二次曲线
的方程:
.
(1)分别求出方程表示椭圆和双曲线的条件:
(2)若双曲线
与直线
有公共点且实轴最长,求双曲线方程:
(3)
、
为正整数,且
,是否存在两条曲线
,其交点
与点
满足
?若存在,求
、
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f219575dd7bb6c3d8912a0d6d81a294.png)
(1)分别求出方程表示椭圆和双曲线的条件:
(2)若双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94555857a26590865f337f8c4a93c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
(3)
![](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/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e00a9e5172c28e6895801dc9c53134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d51de84ea16fc5553ba3d588f379f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce67f2138e7295cd72d66b2908cb6de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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10卷引用:上海市嘉定区第二中学2020-2021学年高二上学期第二次月考数学试题
上海市嘉定区第二中学2020-2021学年高二上学期第二次月考数学试题(已下线)高二期末押题02-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市宝山中学2021-2022学年高二下学期线上期中数学试题上海市建平中学2023届高三上学期11月月考数学试题上海市闵行(文绮)中学2023届高三下学期开学学情调研数学试题福建省永春第一中学2021-2022学年高二上学期期末考试数学试题沪教版(2020) 选修第一册 单元训练 第2章 单元测试沪教版(2020) 选修第一册 高效课堂 第二章 2.3 双曲线(3)(已下线)高二上学期期中【压轴60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)(已下线)第3章 圆锥曲线的方程(基础、典型、易错、新文化、压轴)(2)
名校
解题方法
8 . 已知双曲线C:
的离心率为
,实轴长为2.
(1)求双曲线的标准方程;
(2)若直线
被双曲线C截得的弦长为
,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求双曲线的标准方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
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12卷引用:2014-2015学年重庆市重庆一中高二上学期期中考试理科数学试卷
2014-2015学年重庆市重庆一中高二上学期期中考试理科数学试卷2015-2016学年广东省普宁华侨中学高二上第三次月考文科数学试卷湖南省嘉禾一中、临武一中2017-2018学年高二上学期期中联考数学(文)试题【全国校级联考】福建省闽侯二中五校教学联合体2016-2017学年高二上学期期末考试数学(文)试题四川省成都市武侯区第十二中学2020-2021学年高二上学期10月月考数学试题上海市洋泾中学2022-2023学年高二下学期3月月考数学试题湖北省黄冈市黄梅国际育才高级中学2020-2021学年高二下学期3月月考数学试题重庆市西南大学附属中学校2021-2022学年高二上学期第二次月考数学试题(已下线)专题3.9 直线与双曲线的位置关系-重难点题型精讲-2021-2022学年高二数学举一反三系列(人教A版2019选择性必修第一册)四川省成都外国语学校2022-2023学年高二上学期期中考试数学(文)试题四川省成都外国语学校2022-2023学年高二上学期期中考试数学(理)试题(已下线)第09讲 拓展三:圆锥曲线的方程(弦长问题)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)
名校
解题方法
9 . 已知斜率为
的直线
与抛物线
交于
轴上方不同的两点
、
,记直线
、
的斜率分别为
、
,则
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
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2022-11-19更新
|
473次组卷
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4卷引用:2016届浙江省温州市高三一模理科数学试卷
2016届浙江省温州市高三一模理科数学试卷上海市杨浦区复旦大学附属中学2022-2023学年高二上学期期中数学试题(已下线)重难专攻(八)圆锥曲线中的最值(范围)问题 讲(已下线)考点18 解析几何中的范围、最值问题 2024届高考数学考点总动员【练】
真题
10 . 设是二次曲线C上的点,且
构成了一个公差为
的等差数列,其中O是坐标原点.记
.
(1)若C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f174fd94fbbaa6153157d6bf001724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec5aa21a4fe7170bf7265265de4fb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4886535740a0f54ca39b882d433cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
(2)若C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d83c1c494a901e6a225b1f36ad334c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)请选定一条除椭圆外的二次曲线C及C上的一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db4fe79b98486f0d4556f37d64d74f9.png)
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