名校
1 . 已知椭圆
的中心在坐标原点,焦点在坐标轴上,且经过
、
、
三点.
(1)求椭圆
的方程;
(2)若直线
:
(
)与椭圆
交于
、
两点,证明直线
与直线
的交点在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1a9e36acc58e3af2a826f4cb3a53a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2767866dc6472299128b8bd074e384fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044abd5a93cb0392e5727c29faa2f4d2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5510207df7154e4f25fbe8722441313.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f34291a09fe6b5611a4f293c1004a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
您最近一年使用:0次
2016-12-04更新
|
582次组卷
|
4卷引用:2015-2016学年广东仲元中学高二上学期期中理科数学试卷
2015-2016学年广东仲元中学高二上学期期中理科数学试卷江西省九江第一中学2018-2019学年高二上学期第二次月考数学(理)试题(已下线)专题9.9 圆锥曲线的综合问题(精练)-2021年高考数学(理)一轮复习讲练测海南省海南中学白沙学校2022-2023学年高二下学期期末考试数学试题
2010·河南开封·一模
2 . 如图所示,已知
、
、
是椭圆
上三点,其中点
的坐标为
,
过椭圆的中心
,且
,
.
(1)求点
的坐标及椭圆
的方程;
(2)若椭圆
上存在两点
、
,使得
的平分线总垂直于
轴,试判断向量
与
是否共线,并给出证明.
![](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/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f809aef106f5da271c4800b261a628f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd69522689b9418afd0c85a858322dd.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若椭圆
![](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/030314ca026d6b18481682f70f48d19b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e00e4e17dc8a2ef88e23e348439edf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://img.xkw.com/dksih/QBM/2010/9/27/1569841377214464/1569841382629376/STEM/5e5b3370-c408-488c-af5e-3da54a21164b.png?resizew=241)
您最近一年使用:0次
2010·山东聊城·二模
解题方法
3 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
、
,点
关于
轴的对称点
(
与
不重合),则直线
与
轴是否交于一定点?若是,请写出定点坐标,并证明你的结论;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1497ffc1b18295b5f12c4a566a3285e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f99bddac58806e0024a1268378fe53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51698f7095e795d4f0527b986ac1db2.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4167feb456b79187e3582a90bdc0ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4167feb456b79187e3582a90bdc0ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5427b3e28d3a34a59e2f7ceacd3d5f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2016-11-30更新
|
1532次组卷
|
10卷引用:山东省聊城市2010届高三二模理科数学试题
4 . 直线
与椭圆
交于
两点,已知
,若
且椭圆的离心率
,又椭圆经过点
,
为坐标原点.
(1)求椭圆的方程;
(2)若直线
过椭圆的焦点
(
为半焦距),求直线
的斜率
的值;
(3)试问:
的面积是否为定值?如果是,请给予证明;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e41f14b829a90b38a5cb12975ccec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ee59964f020fc52b5ba66a3f5fcc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091b43a8abc57a695a37c2884845c6d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925752b294d622b2386a885ff67382bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)试问:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
12-13高三·天津·阶段练习
解题方法
5 . 已知椭圆
的一个焦点为
且过点
.
![](https://img.xkw.com/dksih/QBM/2018/8/22/2015983746736128/2016726972760064/STEM/35a34bb8ba694bc68badacce0e4c9699.png?resizew=222)
(Ⅰ)求椭圆
的方程;
(Ⅱ)设椭圆
的上下顶点分别为
是椭圆上异于
的任一点,直线
分别交
轴于点
,若直线
与过点
的圆
相切,切点为
.
证明:线段
的长为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27208f7c8d1f32587bcb0a52dbc40c56.png)
![](https://img.xkw.com/dksih/QBM/2018/8/22/2015983746736128/2016726972760064/STEM/35a34bb8ba694bc68badacce0e4c9699.png?resizew=222)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bebf4417f17ba00e6e1f98ff4c5717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941580b384bf5aa122b56dec5f0e5cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be452c8bdea6b4e4c7a6d96e9dc6a51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
证明:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
您最近一年使用:0次
2016-12-02更新
|
1250次组卷
|
3卷引用:2013届天津市天津一中高三第四次月考文科数学试卷
6 . 设椭圆
过点
,且左焦点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45349f54f6abc8d331556557255f024.png)
(Ⅰ)求椭圆
的方程;
(Ⅱ)当过点
的动直线
与椭圆
相交与两不同点
时,在线段
上取点
,满足
,证明:点
总在某定直线上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e6a574b9fa0d4eaa2619d99ee3da9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45349f54f6abc8d331556557255f024.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)当过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53679be20ae56723e1ecb77ebf0ebe59.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b172e13a3885f10603571b213527726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2016-11-30更新
|
6766次组卷
|
14卷引用:2008年普通高等学校招生全国统一考试理科数学(安徽卷)
2008年普通高等学校招生全国统一考试理科数学(安徽卷)2008 年普通高等学校招生考试数学(理)试题(安徽卷)(已下线)2014届重庆市第八中学高三第四次月考理科数学试卷【全国百强校】四川省南充市阆中中学2018-2019学年高二3月月考理科数学试题【全国百强校】四川省南充市阆中中学2018-2019学年高二3月月考文科数学试题沪教版(上海) 高三年级 新高考辅导与训练 第十一章 圆锥曲线 三、参数方程(已下线)专题12 解析几何中的定值、定点和定线问题 第一篇 热点、难点突破篇(讲)-2021年高考数学二轮复习讲练测(浙江专用)(已下线)专题7 圆锥曲线之极点与极线 微点1 圆锥曲线之极点与极线(已下线)专题7 圆锥曲线之极点与极线 微点2 极点与极线问题常见模型总结(已下线)专题41 定比点差法、齐次化、极点极线问题、蝴蝶问题(已下线)第五篇 向量与几何 专题5 调和点列 微点2 调和点列(二)(已下线)第五篇 向量与几何 专题6 调和线束 微点1 调和线束(一)(已下线)专题18 圆锥曲线高频压轴解答题(16大核心考点)(讲义)-2(已下线)大招16极点极线