名校
解题方法
1 . 已知椭圆
过点
,离心率为
.
(1)求椭圆
的方程;
(2)直线
与椭圆交于
、
两点,过
、
作直线
的垂线,垂足分别为
、
,点
为线段
的中点,
为椭圆
的左焦点.求证:四边形
为梯形.
![](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/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29765ee1897b52c206bae688ded884d.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b556b1a9944719cf423e90f8df16c773.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](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/19a90b911f686685fc0033b085639811.png)
您最近一年使用:0次
2022-01-24更新
|
3894次组卷
|
14卷引用:山西省运城市景胜中学2021-2022学年高二下学期5月月考数学试题
山西省运城市景胜中学2021-2022学年高二下学期5月月考数学试题北京市通州区2022届高三上学期期末数学试题湖北省十一校2022届高三下学期第二次联考数学试题(已下线)数学-2022年高考考前押题密卷(新高考Ⅰ卷)福建省厦门第一中学2021-2022学年高二下学期期中考试数学试题江苏省2022届高三高考前临门一脚数学试题北京市海淀区首都师范大学附属中学2022届高三下学期三模练习数学试题广西南宁市第三中学2022届高三二模数学(文)试题湖南省岳阳市岳阳县2022届高三下学期高考适应性考试数学试题福建省永安第九中学2023届高三上学期期中考试数学试题陕西省咸阳市武功县普集高级中学2022-2023学年高三上学期12月阶段性检测文科数学试题(已下线)大题强化训练(9)北京卷专题23平面解析几何(解答题部分)福建省福州市六校2023-2024学年高二上学期期末联考数学试题
2 . 已知
为坐标原点,椭圆
:
上一点
在第一象限,若
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/4090e3a8-baa3-49cb-98ca-c64f496f7222.png?resizew=176)
(1)求点
的坐标;
(2)椭圆
两个顶点分别为
,
,过点
的直线
交椭圆
于点
,交
轴于点
,若直线
与直线
相交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a619f432ee11b2310ca213f4e8e8a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ea531c752749c6072edd2179822d44.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/4090e3a8-baa3-49cb-98ca-c64f496f7222.png?resizew=176)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242dc4cf2720b503e26ec8017d31444f.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9cbc334d6f4b6f92ffdeba67ca441b8.png)
您最近一年使用:0次
名校
解题方法
3 . 已知椭圆
的离心率为
,
、
分别是椭圆的左、右焦点,
是椭圆上一点,且
的周长是6.
(1)求椭圆
的方程;
(2)设直线
经过椭圆的右焦点
且与
交于不同的两点
,
,试问:在
轴上是否存在点
,使得直线
与直线
的斜率的和为定值?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2020-10-08更新
|
1268次组卷
|
9卷引用:山西省运城市2021届高三上学期9月调研数学(文)试题
名校
解题方法
4 . 顺次连接椭圆
的四个顶点得到边长为
的菱形,该菱形对角线长度之比为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da99c7af03730df7a964485b7394c33f.png)
(1)求椭圆
的标准方程;
(2)设椭圆
的右焦点为
,定点
,过点
的直线
与椭圆
交于两点
,
,设直线
的斜率分别为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da99c7af03730df7a964485b7394c33f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/55fb7ec4aa413693f4ecae59fe0e2084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2020-07-19更新
|
532次组卷
|
2卷引用:2020届山西省运城市高中联合体高三模拟(四)数学(理)试题
解题方法
5 . 椭圆
的焦点为
和
,过
的直线
交
于
两点,过
作与
轴垂直的直线
,又知点
,直线
记为
,
与
交于点
.设
,已知当
时,
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)求证:无论
如何变化,点
的横坐标是定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cfd56cd81719d6adcf2dc655c86b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdae78f4d3b8d8213ac3ac9a9567eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9fce9427c9b17e4d3cda0c3ff3e2e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b58d0185b95b8cf0df6aa712f19fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb2ae1f98558a63702db77ad9f1d5d6.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)求证:无论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2020-05-05更新
|
233次组卷
|
2卷引用:山西省太原市2019-2020学年高三下学期模拟(一)数学(文)试题
2012·广东深圳·一模
名校
解题方法
6 . 如图,在平面直角坐标系xOy中,已知椭圆
的离心率为
,以椭圆C左顶点T为圆心作圆
,设圆T与椭圆C交于点M与点N.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/dc1271f6-ae4f-4681-b3bf-27498f592d5c.png?resizew=308)
(1)求椭圆C的方程;
(2)求
的最小值,并求此时圆T的方程;
(3)设点P是椭圆C上异于M,N的任意一点,且直线MP,NP分别与x轴交于点R,S,O为坐标原点,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f917c606f7883cff799fc35ec068ee8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/dc1271f6-ae4f-4681-b3bf-27498f592d5c.png?resizew=308)
(1)求椭圆C的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fa4729c5ac7062d40bbcf3e49312d2.png)
(3)设点P是椭圆C上异于M,N的任意一点,且直线MP,NP分别与x轴交于点R,S,O为坐标原点,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2382c2608298c372d89106b359c0f495.png)
您最近一年使用:0次
2020-04-18更新
|
1183次组卷
|
14卷引用:【全国百强校】山西省平遥中学2019届高三12月月考数学(理)试题
【全国百强校】山西省平遥中学2019届高三12月月考数学(理)试题(已下线)2012届广东省深圳市高三第一次调研理科数学(已下线)2014届广东省“十校”高三第一次联考理科数学试卷(已下线)2013-2014学年山东济宁任城一中高二上期中检测理科数学试卷(已下线)2014届山东省菏泽市高三3月模拟考试文科数学试卷(已下线)2014届广东省东莞市高三第二次模拟考试文科数学试卷2016届陕西省西安市铁一中学高三下学期开学考试文科数学试卷2015-2016学年吉林省延边二中高二上期末理科数学试卷陕西省西安市长安区第一中学2016-2017学年高二下学期期中考试数学(文)试题江苏省南京市秦淮区2018-2019学年高三下学期第三次模拟考试数学试题江苏省泰州市第二中学2020届高三下学期5月学情调研数学试题吉林省吉林市吉林第一中学2020-2021学年高二上学期阶段性考试数学试题(已下线)专题3-5 圆锥曲线定值问题(已下线)第五篇 向量与几何 专题8 帕斯卡定理、布列安桑定理、笛沙格定理、彭塞列闭合定理 微点3 笛沙格定理、彭塞列闭合定理
名校
解题方法
7 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆
的方程;
(2)过点
的直线交椭圆于
、
两点,若
,在线段
上取点
,使
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c96b59b8f6b4961fd8792c64eec4e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0471cd3dccabaef113cd5761544d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.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/9ff2f7d6d39ee892560459a85412eb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d4820802e89b24615bbc3bc9d0e657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2020-03-29更新
|
2816次组卷
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14卷引用:山西省太原市第五中学2020届高三下学期6月月考数学(理)试题
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8 . 已知
为椭圆
的左、右焦点,点
在椭圆上,且过点
的直线l交椭圆于A,B两点,
的周长为8.
(1)求椭圆E的方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29bf0cf2f9b056030f17dfba06f62b1f.png)
(1)求椭圆E的方程;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9a2d1cb3661943a41b30343a5c2f7e.png)
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2020-03-21更新
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487次组卷
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3卷引用:山西省临汾市2020届高三下学期模拟考试(3)数学(文)试题
山西省临汾市2020届高三下学期模拟考试(3)数学(文)试题(已下线)专题01 解析几何(第三篇)-备战2020高考数学黄金30题系列之压轴题(新课标版)江西省南康区唐江中学2021届高三综合性考试数学(理)试题
解题方法
9 . 已知椭圆
的右焦点
到直线
的距离为
,
在椭圆
上.
(1)求椭圆
的方程;
(2)若过
作两条互相垂直的直线
,
是
与椭圆
的两个交点,
是
与椭圆
的两个交点,
分别是线段
的中点试,判断直线
是否过定点?若过定点求出该定点的坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04836ba2906cf6f1e9aecd2a00824aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05394594e0e50ff41ac1cd74365eaf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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10 . 已知椭圆
的离心率为
,其右焦点
到直线
的距离为
.
(1)求椭圆
的方程;
(2)若过
作两条互相垂直的直线
,
是
与椭圆
的两个交点,
是
与椭圆
的两个交点,
分别是线段
的中点,试判断直线
是否过定点?若过定点,求出该定点的坐标;若不过定点.请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04836ba2906cf6f1e9aecd2a00824aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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