1 . 已知椭圆
过
和
两点.
(1)求椭圆C的方程;
(2)如图所示,记椭圆的左、右顶点分别为A,B,当动点M在定直线
上运动时,直线
,
分别交椭圆于两点P和Q.
(i)证明:点B在以
为直径的圆内;
(ii)求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3b9c17a6c72536ab24b1506cf61a66.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/f1cd9ffc-749f-4803-b4b8-f4fb5693a49f.png?resizew=200)
(1)求椭圆C的方程;
(2)如图所示,记椭圆的左、右顶点分别为A,B,当动点M在定直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
(i)证明:点B在以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(ii)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
您最近一年使用:0次
2023-09-19更新
|
1769次组卷
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9卷引用:第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)
(已下线)第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)湖南省长沙市第一中学2024届高三上学期月考(二)数学试题(已下线)高二上学期期中复习【第三章 圆锥曲线的方程】十二大题型归纳(拔尖篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)广东省佛山市南海区九江中学2024届高三上学期10月月考数学试题湖南省衡阳市衡阳县第二中学2023-2024学年高二上学期期中数学试题四川省资阳市乐至中学2023-2024学年高二上学期期中数学试题江西省宜春市丰城市第九中学2024届高三上学期12月月考数学试题(已下线)重难点突破07 圆锥曲线三角形面积与四边形面积题型全归类(七大题型)(已下线)重难点突破15 圆锥曲线中的圆问题(四大题型)
解题方法
2 . 已知椭圆
的左焦点为
,且点
在椭圆
上.
(1)求椭圆
的标准方程;
(2)椭圆
的上、下顶点分别为
,点
,若直线
与椭圆
的另一个交点分别为点
,证明:直线
过定点,并求该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813f9a2814013e2407b5b1c216159359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb50ceaf1e64c741aee72f89f13c30e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a454d4429bc3accac15dbd154315db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
您最近一年使用:0次
2023-09-17更新
|
947次组卷
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7卷引用:第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)
(已下线)第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)广西壮族自治区玉林市玉林市高三联考2024届高三上学期开学考试数学试题(已下线)高二上学期期中考试解答题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(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(压轴题专练)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)3.1.2 椭圆的简单几何性质(10大题型)精练-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)专题23 椭圆的简单几何性质10种常见考法归类(3)
3 . 已知椭圆E:
,四点
,
,
,
中恰有三点在椭圆E上.
(1)求椭圆E的方程;
(2)点P为椭圆E上的一动点,设直线PA,PB的斜率分别为
,
.
①求
的值;
②若不与坐标轴垂直的直线l交椭圆E于M,N两点,O为坐标原点,
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ca02f2549acffefc06eb0d442b5f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32cabbde0dca483cb9a4457b272cd0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e2fc39db609b1b8d26de387dccb08a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5a49b8191e84cc70e5eb8c7dd626b1.png)
(1)求椭圆E的方程;
(2)点P为椭圆E上的一动点,设直线PA,PB的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
②若不与坐标轴垂直的直线l交椭圆E于M,N两点,O为坐标原点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45f36609bddec6fdabd86e7d5199cbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def5af4970c82399744386f7640dafe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
的两个焦点与短轴的一个端点是直角三角形的三个顶点,且椭圆
过
,直线
与椭圆
交于
、
.
(1)求椭圆
的标准方程;
(2)设直线
、
的斜率分别为
、
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e28e94a16c1bac067b639083c2bd4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.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/83d200a411fbc2f50ad72f1fd729a7d7.png)
您最近一年使用:0次
2023-09-07更新
|
858次组卷
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7卷引用:第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)
(已下线)第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)四川省蓬溪中学校2022-2023学年高二下学期第二次质量检测数学(文)试题河北省唐县第一中学2023-2024学年高二上学期第一次考试(9月)数学试题(已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员江西省南昌市第十中学2023-2024学年高二上学期期中考试数学试题(已下线)重庆市巴蜀中学2024届高三上学期适应性月考(二)数学试题变式题19-22福建省三明市第一中学2023-2024学年高二上学期12月月考数学试题
5 . 已知椭圆
的一个焦点为
,且过点
.
(1)求椭圆
的方程;
(2)直线
与椭圆
交于
两点,求
面积的最大值及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f11c964b3a008d35fb4b3ac18ed5a5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc68ef6b89afc972832cfca71a5b120.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/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2023-08-27更新
|
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3卷引用:江苏省连云港市灌南高级中学2023-2024学年高三上学期第一次月考数学试题
江苏省连云港市灌南高级中学2023-2024学年高三上学期第一次月考数学试题江西省南昌市外国语学校2024届高三上学期8月月考(第一次保送考试)数学试题(已下线)人教A版2019选择性必修第一册综合测试(基础)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)
名校
解题方法
6 . 已知中心在原点的椭圆
右焦点
,点
为椭圆
上一点.
(1)求
的方程;
(2)过点
的两条直线分别交椭圆
于
、
两点,且满足
,问:直线
是否过定点,如果过定点,请求出定点坐标,如果不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.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/0b768ea6a05cbf45b28fc46c501ba532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
解题方法
7 . 已知
,
分别为椭圆
:
的左,右顶点,椭圆
过点
,且离心率为
.
(1)求椭圆
的标准方程;
(2)若
为椭圆上异于
,
的一点,且直线
,
分别与直线
:
相交于
,
两点,且直线
与椭圆
交于另一点
,证明:
,
,
三点共线.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.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/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
8 . 已知椭圆
过点
,且离心率为
.
(1)求
的方程;
(2)若点
,直线
与椭圆
交于两点
、
,且与
轴交于点
,连接
和
.从下列三个条件中选取一个作为条件,探究直线
是否过定点,如果是,请求出定点,如果不是,请说明理由.
①点
关于
轴的对称点在直线
上;
②若直线
与直线
的倾斜角分别为
、
,且满足
;
③
、
两点不在
轴上,设
和
的面积分别为
和
,且
.
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c179fe7eff7abfdd092b63c9c1b82d0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a072f7e07dcefc3db2a0443214eedaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1dbab7580d1671f4d5fa8cfa5c5e981.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/bf6b4539674e585ecd20d20e8974b611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4088a93100186f0510eba81f962ba90e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39931f7165558c636da27ca0f5765182.png)
注:如果选择多个条件分别解答,按第一个解答计分.
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解题方法
9 . 已知椭圆
的离心率为
,且点
在椭圆
上.
(1)求椭圆
的标准方程;
(2)斜率为正数
且不过原点的直线
交椭圆
于
两点,线段
的中点为
,射线
交椭圆
及直线
分别于点
和点
,且
.证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04443a0c1cf4808aea741c9f9379b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3230e05b8cbfc2abb93f39941c91ce37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率为正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5681ab21c52a2bcf314220431c777945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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10 . 设椭圆
过点
,
两点,
为坐标原点.
(1)求椭圆
的标准方程;
(2)是否存在圆心为原点的圆,使得该圆的任意一条切线与椭圆
恒有两个交点
,
,且
?若存在,写出该圆的方程,并求
的取值范围,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ad4a60e2b50a820ec2044aa55f2472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e17bb6c058ffb1b86b215a582e98e663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)是否存在圆心为原点的圆,使得该圆的任意一条切线与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/dc4876efa91f38d11ce12fed2e1fbf2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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