2012·湖北襄阳·一模
1 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
的离心率为
,以原点为圆心,椭圆的短半轴为半径的圆与直线
相切,过点
且不垂直于x轴直线
与椭圆C相交于A、B两点.
(1)求椭圆C的方程;
(2)求
的取值范围;
(3)若B点关于x轴的对称点是E,证明:直线AE与x轴相交于定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38f9106cef0b638e62c90afc1c523cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c153027427477bcd0a7228b14ce96cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求椭圆C的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ace585d3cc2e113a0927cdf9e56756a.png)
(3)若B点关于x轴的对称点是E,证明:直线AE与x轴相交于定点.
您最近一年使用:0次
2016-12-02更新
|
1176次组卷
|
8卷引用:2016届四川省成都市七中高三11月段测三理科数学试卷
2016届四川省成都市七中高三11月段测三理科数学试卷2016届四川省成都市七中高三11月段测三文科数学试卷2016届四川省成都市七中高三11月阶段测试理科数学试卷2016届四川省成都市七中高三11月阶段测试文科数学试卷(已下线)2012届湖北省襄阳市高三3月调研考试数学理科试卷(已下线)2014届人教版高考数学文科二轮专题复习提分训练22练习卷(已下线)2011-2012学年湖北省荆门市高二下学期期末质量检测理科数学试卷福建省三明市第一中学2017-2018学年高二上学期期中考试数学(文)试题2
2014·四川成都·一模
解题方法
2 . 已知椭圆
的离心率为
,点
在椭圆上.
(I)求椭圆C的方程;
(II)设椭圆的左右顶点分别是A、B,过点
的动直线与椭圆交于M,N两点,连接AN、BM相交于G点,试求点G的横坐标的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db81446766bb8f493d6fc49e65f0d495.png)
(I)求椭圆C的方程;
(II)设椭圆的左右顶点分别是A、B,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f579b73ca01978ec68e716f993bc3766.png)
您最近一年使用:0次
2014·四川成都·一模
3 . 已知椭圆C:
(
)的短轴长为2,离心率为
.
(1)求椭圆C的方程
(2)若过点M(2,0)的引斜率为
的直线与椭圆C相交于两点G、H,设P为椭圆C上一点,且满足
(O为坐标原点),当
时,求实数
的取值范围?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374d3462754e846cbb0f7dd5fd28277.png)
![](https://img.xkw.com/dksih/QBM/2014/4/23/1571643996987392/1571644002721792/STEM/7ee3d6ff83964d4e978f08f1c9f757a0.png)
(1)求椭圆C的方程
(2)若过点M(2,0)的引斜率为
![](https://img.xkw.com/dksih/QBM/2014/4/23/1571643996987392/1571644002721792/STEM/c13f7c4c0c3c418f875284f6d97f7768.png)
![](https://img.xkw.com/dksih/QBM/2014/4/23/1571643996987392/1571644002721792/STEM/d5bdfc00a1664a0181651d847a5d3751.png)
![](https://img.xkw.com/dksih/QBM/2014/4/23/1571643996987392/1571644002721792/STEM/a1551437bdea4b7abab6a8f889bd5eaf.png)
![](https://img.xkw.com/dksih/QBM/2014/4/23/1571643996987392/1571644002721792/STEM/00a59cde528c4af38450796b6015251b.png)
您最近一年使用:0次
13-14高三下·四川成都·阶段练习
名校
解题方法
4 . 椭圆
的两焦点坐标分别为
和
,且椭圆经过点
.
(1)求椭圆
的标准方程;
(2)过点
作直线
交椭圆
于
两点(直线
不与
轴重合),
为椭圆的左顶点,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64e6710b63be834229f41a03185ad4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ba3ceae4e590e0b45e9f416af8dd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b831437110ef3fb0fcf138dec726c779.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910c141903e61562f091553950981608.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/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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8feee30fadc432deace534d528feb16b.png)
您最近一年使用:0次
12-13高三·四川内江·阶段练习
解题方法
5 . 已知椭圆
过点
,离心率为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)过点
且斜率为
(
)的直线
与椭圆
相交于
两点,直线
、
分别交直线
于
、
两点,线段
的中点为
.记直线
的斜率为
,求证:
为定值.
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/c0f903842bbd4fa4b7d3fedcf0614fd0.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/609c9752a2894962bd5adbd641be4c4d.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/11560dbae8e64a9e8c86e6d642e5d2f5.png)
(Ⅰ)求椭圆
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/f08248a86e3e4468a47ff8953e0f26a3.png)
(Ⅱ)过点
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/e23362c6c7d44fa68774d809a56fc3cc.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/d6e33d7ac9b14d28b8c5fd263f22b597.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/3b5c3a2e366d4a8c846959d8166b8276.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/cb79045227cb48eb91f0c6b5d099e6fb.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/f08248a86e3e4468a47ff8953e0f26a3.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/931e9b22456e4e2b885d9c05315ed0c1.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/5934e595a8c44efeb4a5e43153c70cb9.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/d272ee9001a14ba6aee5854d207cbdec.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/e50da1fa4e71418dbfd50eb527befb8e.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/24ba6e5dd95f4184bceab10037b5785b.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/bb739ce9dda949a99fa7c2f7fc648956.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/6ff9c48cc36b4db9b0c7b26d0db8c299.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/4c7a391e777c435199a8132733b25609.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/98f87aa421104214af505f5925795237.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/f08fdbdd580341bd828bace35951125b.png)
![](https://img.xkw.com/dksih/QBM/2013/11/26/1571403986108416/1571403992047616/STEM/d69fe53cb4dd476c9da49c51266e1229.png)
您最近一年使用:0次
6 . 已知圆M:(x+1)2+y2=1,圆N:(x-1)2+y2=9,动圆P与圆M外切并与圆N内切,圆心P的轨迹为曲线 C
(1)求C的方程;
(2)l是与圆P,圆M都相切的一条直线,l与曲线C交于A,B两点,当圆P的半径最长时,求|AB|.
(1)求C的方程;
(2)l是与圆P,圆M都相切的一条直线,l与曲线C交于A,B两点,当圆P的半径最长时,求|AB|.
您最近一年使用:0次
2016-12-02更新
|
8463次组卷
|
19卷引用:2017届四川双流中学高三必得分训练7数学试卷
2017届四川双流中学高三必得分训练7数学试卷四川省仁寿第一中学北校区2020届高三下学期第二次高考模拟数学(文)试题2013年全国普通高等学校招生统一考试理科数学(新课标1卷)2013年全国普通高等学校招生统一考试文科数学(新课标1卷)2015届江西省南昌市第三中学高三上学期第四次月考理科数学试卷上海市五校2016届高三上学期12月联考(理科)数学试题2020届湖南省长沙市长郡中学高三第二次月考数学(文)试题甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(文)试题(已下线)秒杀题型13 圆锥曲线中的轨迹-2020年高考数学试题调研之秒杀圆锥曲线压轴题山西省太原市第五中学2021届高三下学期二模数学(文)试题(已下线)收官卷02--备战2022年高考数学(文)一轮复习收官卷(全国乙卷)(已下线)收官卷02--备战2022年高考数学(文)一轮复习收官卷(全国甲卷) (已下线)专题17 解析几何解答题湖南省永州市第一中学2022-2023学年高三上学期第二次月考数学试题江苏省连云港市五校2023-2024学年高三上学期12月联考数学试题2015-2016学年吉林实验中学高二上学期期中文科数学试卷广东省佛山市第一中学2019-2020学年高二上学期第二次段考数学试题辽宁省大连市红旗高级中学2020-2021学年高二上学期期中数学试题河南省南阳市六校2023-2024学年高二上学期第一次联考数学试题
7 . 已知椭圆
的离心率为
,以原点为圆心,椭圆的短半轴为半径的圆与直线
相切,直线
与椭圆C相交于A、B两点.
(Ⅰ)求椭圆C的方程;
(Ⅱ)求
的取值范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2f2d391b1e6304eb2bba560d0ccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83236e9439d49bdf9f3baf621e7b1eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f13a4dfa82ef9ca147570fd19fb94fc.png)
(Ⅰ)求椭圆C的方程;
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525a5bbe51ff7f161be5164ca0b36efe.png)
您最近一年使用:0次
2013·四川成都·一模
解题方法
8 . 在直角坐标系内,点
实施变换
后,对应点为
,给出以下命题:
①圆
上任意一点实施变换
后,对应点的轨迹仍是圆
;
②若直线
上每一点实施变换
后,对应点的轨迹方程仍是
则
;
③椭圆
上每一点实施变换
后,对应点的轨迹仍是离心率不变的椭圆;
④曲线
:
上每一点实施变换
后,对应点的轨迹是曲线
,
是曲线
上的任意一点,
是曲线
上的任意一点,则
的最小值为
.
以上正确命题的序号是__________________ (写出全部正确命题的序号).
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/d99aba99db7e47f295af142809522616.png?resizew=51)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/1de0247fee2a4ff9aa29366a04bfc230.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/4921e63abb3f40f5aa42bdc14f3420ec.png?resizew=55)
①圆
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/aa280e6833cb4f73bc519b4435f2a237.png?resizew=129)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/1de0247fee2a4ff9aa29366a04bfc230.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/1873448be18f4ca38b847b583f49c683.png?resizew=84)
②若直线
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/041dc3219a71460d8e0664c4c78e93f5.png?resizew=69)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/1de0247fee2a4ff9aa29366a04bfc230.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/06078ec94cfa4e08ac09a7942bc61b63.png?resizew=72)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/9b802b623c0c4279ab7d367bc0e044cc.png?resizew=45)
③椭圆
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/f2279902fc5e4fc9a372e96354aabfda.png?resizew=151)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/1de0247fee2a4ff9aa29366a04bfc230.png?resizew=16)
④曲线
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/aadda85bf1f941af8f441489a9e34846.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/ea6fbc2ad54248189a054346f6355324.png?resizew=121)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/1de0247fee2a4ff9aa29366a04bfc230.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/ccb834161738402a8a84f9d681d98827.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/55aea85c3fd44755ae29e239812f109e.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/aadda85bf1f941af8f441489a9e34846.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/434002cace91489ab529977e5802fcc8.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/ccb834161738402a8a84f9d681d98827.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/244f222f595944039716effe0db4ebc8.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2013/8/29/1571332578451456/1571332583661568/STEM/097b96339a26405ca9ae3d4ab3b0ba64.png?resizew=80)
以上正确命题的序号是
您最近一年使用:0次
名校
9 . 已知椭圆
的一个焦点为
,左右顶点分别为
,经过点
的直线
与椭圆
交于
两点.
(1)求椭圆方程;
(2)记
与
的面积分别为
和
,求
的最大值.
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/3bf8c8e2c76a46eb9ddee6bdabafedd2.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/e64a967f6db340b2a0134c16fdec6e6d.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/757e842ae7894aaa8e9f0f7ca20209da.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/91d4f6152bb84006a5dcceda10e74725.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/8345e5bed6a540468822defd530bd38c.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/225cc03fcc4e43d6994e77a95a5f9482.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/11f390dbe0cf430787e50b4e13c57383.png)
(1)求椭圆方程;
(2)记
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/d2fa589317584b5d9c00db8a5fb57a47.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/9508316878a54b218516dddddc64f007.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/74e74ed61b794144a5244ccf8da412fe.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/1bfd94f973d34c00902ceb4d627f3383.png)
![](https://img.xkw.com/dksih/QBM/2016/6/1/1572685908099072/1572685914021888/STEM/cd52fb2a2b2149c1b52b14366e5a0107.png)
您最近一年使用:0次
2016-01-22更新
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530次组卷
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5卷引用:2017届四川巴中市高中高三毕业班10月零诊理数试卷
11-12高三上·云南红河·阶段练习
10 . 如图,曲线
是以原点O为中心、
为焦点的椭圆的一部分,曲线
是以O为顶点、
为焦点的抛物线的一部分,A是曲线
和
的交点
且
为钝角.
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037241856/STEM/2bdd357090ad4775843cd6bfbd681cf1.png)
(1)求曲线
和
的方程;
(2)过
作一条与
轴不垂直的直线,分别与曲线
依次交于B、C、D、E四点,若G为CD中点、H为BE中点,问
是否为定值?若是求出定值;若不是说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/3ceb0061dbf8f720f8d0bee5ca5c822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0613f3bc4f0cd9f81cbb7ebf5f4ae9.png)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037241856/STEM/2bdd357090ad4775843cd6bfbd681cf1.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/2012/9/13/1571014031548416/1571014037241856/STEM/364510c64a3d410c8244439a74ca99d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86404c0a62742241d6d772b9cb657b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03c37a89b5adc2eb1aba1f37fab2bd12.png)
您最近一年使用:0次