名校
解题方法
1 . 已知椭圆
的左右顶点为A、B,右焦点为F,C为短轴一端点,
的面积为
,离心率为
.
(1)求椭圆的标准方程:
(2)过点F的直线交椭圆于M,N两点(异于A,B),直线AM与BN的交点为Q.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆的标准方程:
(2)过点F的直线交椭圆于M,N两点(异于A,B),直线AM与BN的交点为Q.
①求证:Q点在定直线上;
②求证:射线FQ平分∠MFB.
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2022-12-15更新
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1116次组卷
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5卷引用:福建省厦门外国语学校石狮分校2022-2023学年高二上学期期中考试数学试题
福建省厦门外国语学校石狮分校2022-2023学年高二上学期期中考试数学试题陕西省西安市西航一中2022-2023学年高二上学期期中数学试题山东省德州市第一中学2022-2023学年高二上学期1月期末数学试题新疆生产建设兵团第六师五家渠高级中学2022-2023学年高二下学期开学考试数学试题(已下线)第五篇 向量与几何 专题11 圆锥曲线中的蝴蝶定理 微点1 圆锥曲线中的蝴蝶定理
2 . 已知圆A:
,T是圆A上一动点,BT的中垂线与AT交于点Q,记点Q的轨迹为曲线C.
(1)求曲线C的方程;
(2)过点(0,2)的直线l交曲线C于M,N两点,记点P(0,
).问:是否存在直线l,满足PM=PN?如果存在,求出直线l的方程;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d91114f380425793cd375cd3994127.png)
(1)求曲线C的方程;
(2)过点(0,2)的直线l交曲线C于M,N两点,记点P(0,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
您最近一年使用:0次
2022-11-09更新
|
636次组卷
|
3卷引用:江苏省南京市2022-2023学年高二上学期期中数学试题
名校
解题方法
3 . 已知椭圆
:
,若点
,
,
,
中恰有三点在椭圆
上.
(1)求
的方程;
(2)点
是
的左焦点,过点
且与
轴不重合的直线
与
交于不同的两点
,
,求证:
内切圆的圆心在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b67c0525a41fffd3ff86fded5ce46c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa147625926cc1453cc20b42f0685a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c591b4f1df5b29cb3e03f136e376c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45213955caa6458ba08ee56153087489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/3ad3a4d8eb0a4f3dd417124a19f60066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/004104bafb5f30338123d4ea2b7fedde.png)
您最近一年使用:0次
2022-11-05更新
|
559次组卷
|
2卷引用:江苏省南京师范大学附属中学2022-2023学年高二上学期期中数学试题
名校
4 . 已知椭圆
过点
,离心率为
.
(1)求椭圆
的方程;
(2)已知定点
,若直线
与椭圆
相交于
、
两点,试判断是否存在实数
,使以
为直径的圆过定点
?若存在求出这个
值,若不存在说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813597f052c8930e12f0a22aeaa3cce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc46e6bd956e9c927cdf5345a7639082.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-01-17更新
|
1335次组卷
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5卷引用:天津市南开大学附属中学2022-2023学年高二上学期期中数学试题
天津市南开大学附属中学2022-2023学年高二上学期期中数学试题(已下线)卷05 高二上学期期中——重难点突破 A卷-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)天津市第二中学2022-2023学年高二上学期12月学情调查数学试题云南省曲靖天人高级中学2022-2023学年高二下学期期中考试数学试题天津市西青区2020-2021学年高二上学期期末数学试题
名校
5 . 设椭圆
的离心率为
,直线
过椭圆的右焦点
,与椭圆交于点
;若
垂直于
轴,则
.
(1)求椭圆的方程;
(2)椭圆的左右顶点分别为
,直线
与直线
交于点
.求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](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/9cbdd945cdadb7dca0d281d791374573.png)
(1)求椭圆的方程;
(2)椭圆的左右顶点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663368000ac90f582d12675aa2d1e832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-01-28更新
|
922次组卷
|
7卷引用:湖南省长沙市长郡湘府中学2022-2023学年高二上学期期中模拟数学试题
名校
6 . 已知椭圆
的左、右顶点分别为
,其离心率
,过点
的直线
与椭圆
交于
两点(异于
),当直线
的斜率不存在时,
.
(1)求椭圆
的方程;
(2)若直线
与
交于点
,试问:点
是否恒在一条直线上?若是,求出此定直线方程,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bbe873760a74d9aedaafc98fe7e83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b28bf947fd9082bd2db8ed3cb82fb15.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2018-02-06更新
|
339次组卷
|
5卷引用:甘肃省兰州市等2地、天水市第三中学等2校2022-2023学年高二上学期期中数学试题
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