名校
解题方法
1 . 已知椭圆
的左、右焦点分别为
,
其中右焦点坐标为
,该椭圆的离心率为
.
(1)求椭圆的标准方程;
(2)已知点
为椭圆上一点,过点
的直线l与椭圆交于异于点P的A,B两点,若
的面积是
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](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/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0632becd411a505efaf6ce37b6aada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed31fe13563364ebcd229b9547d86bd0.png)
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解题方法
2 . 已知椭圆C:
的右焦点为
,且经过点
.
(1)求椭圆C的方程;
(2)直线
:
与椭圆C交于两个不同的点M,N,若线段
中点的横坐标为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
(1)求椭圆C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd21a58f903248cf422d5ae338d1107.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
3 . 已知椭圆C:
与椭圆
有相同的焦点,过椭圆C的右焦点且垂直于x轴的弦长度为1.
(1)求椭圆C的方程;
(2)直线l:
与椭圆C交于A,B两点,若
,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea5ff71e486af6799871a51841f1844.png)
(1)求椭圆C的方程;
(2)直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20238eb22b9189cbe4f736730fad1c18.png)
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2023-10-11更新
|
1542次组卷
|
5卷引用:北京市日坛中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
4 . 已知椭圆
过点
,且椭圆
的离心率为
.
(1)求椭圆
的方程;
(2)若动点
在直线
上,过
作直线交椭圆
于
两点,且
为线段
的中点,再过
作直线
,证明:直线l恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6ee852866de30427eb5fcd52cacbf8.png)
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2023-08-20更新
|
1833次组卷
|
9卷引用:北京大学附属中学2022-2023学年高二下学期期中练习数学试题
北京大学附属中学2022-2023学年高二下学期期中练习数学试题北京市第一○一中学2022-2023学年高二下学期期中练习数学试题北京高二专题01平面解析几何江苏省“四校联盟”2023-2024学年高二上学期9月开学检测数学试题(已下线)3.1.2 椭圆的简单的几何性质(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)吉林省长春市农安县2023-2024学年高三上学期零模调研数学试题(已下线)考点17 解析几何中的定点与定直线问题 2024届高考数学考点总动员(已下线)第三章 圆锥曲线的方程(压轴必刷30题7种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)天津市红桥区2024届高三一模数学试题
名校
解题方法
5 . 已知椭圆E:
过点
,E的离心率
.
(1)求椭圆的标准方程;
(2)设点A、B为椭圆左右顶点,过点
且不与x轴重合的直线l分别交E于C,D.直线
分别交直线AC和BD于P,Q点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
(1)求椭圆的标准方程;
(2)设点A、B为椭圆左右顶点,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d196d17bd2569f9e99a945809d08599b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3b8b374f47492c599241cc866cabe4.png)
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2023-08-05更新
|
560次组卷
|
2卷引用:北京市海淀区清华大学附属中学2022-2023学年高二上学期期中考试数学试题
名校
解题方法
6 . 已知椭圆M:
,圆N:
,直线l过椭圆M右焦点F且倾斜角为
.
(1)求直线l方程及椭圆M的焦距.
(2)直线l交椭圆M于A、B两点,直线l交圆N于C、D两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f4b244b3b0799cfb1994364036eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a10949d80312f0fc9efa3a8e6bd764a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
(1)求直线l方程及椭圆M的焦距.
(2)直线l交椭圆M于A、B两点,直线l交圆N于C、D两点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec33cfe76830902de877bdb208adbb0.png)
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名校
解题方法
7 . 已知椭圆
.
(1)求直线
被椭圆
截得的弦长;
(2)若直线
与椭圆
相切,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e88ab2f7f0cc281e62fbc7e920e0cf1.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.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
名校
8 . 已知椭圆
的一个顶点为
,且离心率为
.
(1)求椭圆C的方程;
(2)直线
与椭圆C交于A、B两点,且
,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆C的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
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2022-11-08更新
|
1147次组卷
|
6卷引用:北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题
北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题吉林省长春市长春外国语学校2022-2023学年高二下学期期中数学试题(已下线)期中真题必刷椭圆60题(4个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)广东省江门市第一中学中2022-2023学年高二上学期第二次段考数学试题上海外国语大学附属外国语学校2022-2023学年高二下学期3月月考数学试题天津市第五十四中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
9 . 已知椭圆
过点
,且离心率为
.设
,
为椭圆
的左、右顶点,
为椭圆上异于
,
的一点,直线
,
分别与直线
相交于
,
两点,且直线
与椭圆
交于另一点
.
(1)求椭圆
的标准方程;
(2)求证:直线
与
的斜率之积为定值;
(3)判断三点
,
,
是否共线?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.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/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)判断三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
名校
解题方法
10 . 椭圆
短轴的上下两个端点分别为
,直线
与
轴、
轴分别交于两点
,交椭圆于两点
.
(1)若
,求直线l的方程;
(2)设直线
的斜率分别为
,
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72eeed455051e355653892f1f8bbfba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6beb510cf91f4479246f62b5dcc1e2f7.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5aefba647642963129d6867930e2fd.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/f81366cdb4230d53e7fb23fc1145b9e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次