名校
1 . 已知椭圆
,点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
(Ⅰ)求椭圆
的短轴长和离心率;
(Ⅱ)过
的直线
与椭圆
相交于两点
,设
的中点为
,判断
与
的大小,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3995288b1519ab38e1b412d91dc8fb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f6816548e716a864e088c962cec576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4066dc453c2e3fa4b08023f76229e0a7.png)
您最近一年使用:0次
2018-01-19更新
|
650次组卷
|
6卷引用:北京市海淀区2018届高三第一学期期末理科数学试题
名校
解题方法
2 . 已知椭圆
的两个焦点分别为
,短轴的两个端点分别为
.
(Ⅰ)若
为等边三角形,求椭圆
的方程;
(Ⅱ)若椭圆
的短轴长为
,过点
的直线
与椭圆
相交于
两点,且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7352dbf2e0740056910e7721bd420d2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/be2356ebff2bbcd1e1926c0019ab72f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2016-12-03更新
|
1558次组卷
|
18卷引用:2015届北京市第四中学高三上学期期中考试文科数学试卷
2015届北京市第四中学高三上学期期中考试文科数学试卷2015-2016学年吉林省吉林一中高二11月月考文科数学卷2015-2016学年湖南省浏阳一中、攸县一中高二上期中理科数学试卷2015-2016学年内蒙古赤峰二中高二上第二次月考文数学卷2017届浙江台州中学高三10月月考数学试卷2016-2017学年河北卓越联盟高二理上学期月考三数学试卷2016-2017学年河北卓越联盟高二文上学期月考三数学试卷黑龙江省齐齐哈尔市实验中学2017-2018学年高二上学期期中考试数学(理)试题黑龙江省齐齐哈尔市实验中学2017-2018学年高二上学期期中考试理科数学试题(已下线)上海市华东师范大学第二附属中学2017届高三上学期期中数学试题甘肃省甘南藏族自治州合作第一中学2019-2020学年高二上学期期末考试数学(理)试题宁夏长庆高级中学2020-2021学年高二上学期期中考试数学(理)试题山西省朔州市怀仁市第一中学2021-2022学年高二上学期第三次月考数学(文)试题山西省朔州市怀仁市第一中学2021-2022学年高二上学期第三次月考数学(理)试题四川省成都市东部新区养马高级中学2022-2023学年高二上学期期中考试数学(理)试题沪教版(2020) 选修第一册 高效课堂 第二章 2.2 椭圆(3)辽宁省辽东南协作校2023-2024学年高二上学期12月月考数学(A卷)试题(已下线)专题7-4圆锥曲线五个方程型大题归类-1
2014·北京朝阳·二模
名校
3 . 已知椭圆
的中心在原点
,焦点在
轴上,离心率为
,右焦点到右顶点的距离为
.
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)是否存在与椭圆
交于
两点的直线
:
,使得
成立?若存在,求出实数
的取值范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)是否存在与椭圆
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14383bf42430ff8c3dc1a68868185cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0679b8e8790352e08a702e1fea3ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-03更新
|
2188次组卷
|
8卷引用:2014届北京市朝阳二模理科数学试卷
(已下线)2014届北京市朝阳二模理科数学试卷(已下线)北京市第四中学2022届高三下学期(三模)保温练习数学试题(已下线)2015届吉林省实验中学高三第四次模拟考试理科数学试卷2015届甘肃省天水市高三一轮复习基础知识检测理科数学试卷2015届江西省高安中学高三命题中心模拟押题一文科数学试卷2016届宁夏银川唐徕回民中学高三下三模理科数学试卷2017届重庆市育才中学高三上学期入学考试数学(文)试卷山东省菏泽市曹县第一中学2022-2023学年高二上学期第一次月考数学试题
名校
4 . 已知点
、
是椭圆
的焦点,
是椭圆上一点,直线
.
(1)求△
的周长;
(2)若直线
与椭圆相切,求
的值;
(3)当
时,直线
与椭圆相交于
、
两点,求弦长
.
![](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/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
(1)求△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5a8e1bc9748e5519dcd9981b7eb251.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/aaff41080fdea43eea7efedf9ebc1498.png)
您最近一年使用:0次
2019-12-31更新
|
304次组卷
|
2卷引用:北京市中央民族大学附属中学2019-2020学年高二上学期期中考试数学试题
名校
5 . 已知椭圆
的右焦点与抛物线
的焦点重合,点
在椭圆
上.
(1)求椭圆
的方程;
(2)设
,直线
与椭圆
交于
两点,若直线
,
均与圆
相切,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67baac84cf5c95d06d50c36cab7c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fbf5844e5482dc00bac45cb50d880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4896f254406ddfe0744b63f10724e76a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2017-05-12更新
|
879次组卷
|
4卷引用:北京市丰台区2017届高三5月综合练习(二模)数学(理)试题
6 . 在平面直角坐标系xOy中,椭圆:
的离心率为
,y轴于椭圆相交于A、B两点,
,C、D是椭圆上异于A、B的任意两点,且直线AC、BD相交于点M,直线AD、BC相交于点N.
求椭圆的方程;
求直线MN的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00df4f17848c072b51e80d427d486e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1680cbefbddcaa13b2e3df8eab7d383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
您最近一年使用:0次
2018-12-20更新
|
333次组卷
|
2卷引用:【全国百强校】北京市清华大学附属中学2018-2019学年高二(上)期中数学试题
名校
7 . 已知椭圆
:
的短轴长为
,右焦点为
,点
是椭圆
上异于左、右顶点
的一点.
(1)求椭圆
的方程;
(2)若直线
与直线
交于点
,线段
的中点为
,证明:点
关于直线
的对称点在直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907d5147cea4c9ce855074864fe54506.png)
您最近一年使用:0次
2017-05-04更新
|
647次组卷
|
7卷引用:北京市东城区2017届高三二模理科数学试题
北京市东城区2017届高三二模理科数学试题北京市东城区2017届高三5月综合练习(二模)数学理试题北京市东城区2017届高三5月综合练习(二模)理数试题(已下线)卷02-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(北京专用)(已下线)卷03-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)湖北省襄阳市第四中学2017届高三高考适应性考试数学(文)试题湖北省襄阳四中2017届高三下学期5月适应性考试数学(文)试题
名校
8 . 如图,点
是椭圆
:
的短轴位于
轴下方的端点,过点
且斜率为1的直线交椭圆于点
,
在
轴上,且
轴,
.
![](https://img.xkw.com/dksih/QBM/2019/5/17/2205499213357056/2206847872770048/STEM/f9935d9688e64af98b13291457b07f93.png?resizew=127)
(1)若点
的坐标为
,求椭圆
的标准方程;
(2)若点
的坐标为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/7f9e8449aad35c5d840a3395ea86df6d.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/84d2cba6875659a46871db6f0010f61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b90fe5c5a937035c7ef20c09bed5cce.png)
![](https://img.xkw.com/dksih/QBM/2019/5/17/2205499213357056/2206847872770048/STEM/f9935d9688e64af98b13291457b07f93.png?resizew=127)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b96dbf02194b5466bc11cb63c874c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2018-01-16更新
|
367次组卷
|
6卷引用:北京市大兴区兴华中学2023届高三上学期12月月考数学试题
北京市大兴区兴华中学2023届高三上学期12月月考数学试题江苏省苏州实验中学2017-2018学年高二上学期第二次月考数学试题步步高高二数学暑假作业:【文】暑假学习效果验收考试步步高高二数学暑假作业:【理】暑假学习效果验收考试福建省福州市闽江口联盟校2020-2021学年高二上学期期中联考数学试题(已下线)检测(四)-【专题突破】2021-2022学年高二数学之圆锥曲线与方程(人教A版选修1-1)
11-12高二上·四川雅安·阶段练习
真题
9 . 如图,已知某椭圆的焦点是F1(-4,0)、F2(4,0),过点F2并垂直于x轴的直线与椭圆的一个交点为B,且|F1B|+|F2B|=10,椭圆上不同的两点A(x1,y1),C(x2,y2)满足条件:|F2A|、|F2B|、|F2C|成等差数列.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/7da7f908-1337-48c7-a56b-398e9cf0063a.png?resizew=160)
(1)求该椭圆的方程;
(2)求弦AC中点的横坐标;
(3)设弦AC的垂直平分线的方程为y=kx+m,求m的取值范围.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/7da7f908-1337-48c7-a56b-398e9cf0063a.png?resizew=160)
(1)求该椭圆的方程;
(2)求弦AC中点的横坐标;
(3)设弦AC的垂直平分线的方程为y=kx+m,求m的取值范围.
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2016-12-01更新
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6卷引用:2002年普通高等学校春季招生考试数学(理)试题(北京卷)
2002年普通高等学校春季招生考试数学(理)试题(北京卷)(已下线)2011—2012学年四川省雅安中学高二12月月考理科数学试卷(已下线)2011-2012学年山东省汶上一中高二12月月考理科数学(已下线)2011-2012学年山东省金乡一中高二上学期12月月考理科数学2014-2015学年山东省潍坊市一中高二上学期1月质量检测数学试卷2014-2015学年山东省潍坊市一中高二1月月考数学试卷
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解题方法
10 . 已知椭圆
的右焦点为
,离心率为
,设直线
的斜率是1,且
与椭圆
交于
,
两点.
(1)求椭圆的标准方程.
(2)若直线
在
轴上的截距是
,求实数
的取值范围.
(3)以
为底作等腰三角形,顶点为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f729f918900b215c9721da1b44efdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2cf93ce94db02356a1429cacc74dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求椭圆的标准方程.
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248909c543977b1a7490bc01fcf44d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2017-10-31更新
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668次组卷
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3卷引用:北京通州潞河中学2016-2017高二上学期期中数学(文)试题