名校
1 . 在平面直角坐标系中,已知
的方程为
,平面内两定点
、
.当
的半径取最小值时:
(1)求出此时
的值,并写出
的标准方程;
(2)在
轴上是否存在异于点
的另外一个点
,使得对于
上任意一点
,总有
为定值?若存在,求出点
的坐标,若不存在,请说明你的理由;
(3)在第(2)问的条件下,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12d59d7e0fc1f1f57b0c336f09eb5fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a62c9695f5a1691c5fe8724fa764b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2930d0f90e573deef7c80f9f0c446604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
(1)求出此时
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591ccce336af06e51e7f4887c287b80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(3)在第(2)问的条件下,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352242e3bd9fc355639cc934bf60c921.png)
您最近一年使用:0次
2018-07-16更新
|
655次组卷
|
2卷引用:上海师范大学附属外国语中学2023届高三模拟数学试题
2 . 已知直线
经过抛物线
的焦点且与此抛物线交于
两点,
,直线
与抛物线
交于
两点,且
两点在
轴的两侧.
(1)证明:
为定值;
(2)求直线
的斜率的取值范围;
(3)已知函数
在
处取得最小值
,求线段
的中点
到点
的距离的最小值(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd63005c9bd42515572bc0369de49ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e51218e05d47d697e3440da34d0c6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d30f14c009f755460915938cba0b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d907557c2d36794cf37a640df86720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94165c5047e68e952df7a8dc6dc32fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94165c5047e68e952df7a8dc6dc32fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcf9bfbf771cb6118f8e631724314e3.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008d0107d9a5539043c29ba8179f1168.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f080380f0785f3a1cd4c6340dbe1dec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307aa7e639a9dfbb937ec625baf22f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8c0b71b1011ff96a18a2a5185dc7ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
您最近一年使用:0次
名校
解题方法
3 . 已知圆
,点
圆
上一动点,
,点
在直线
上,且
,记点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)已知
,过点
作直线
(
不与
轴重合)与曲线
交于
不同两点,线段
的中垂线为
,线段
的中点为
点,记
与
轴的交点为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4dd5f6fad6c5e42c7f4991a701511b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16c2849d99897a32867ab0e31a38e5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f4faed99e8f7100584d50eedea8c1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3259f0ec9307cc5c8a59f03cd0100321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c699a757a7ee06c063150def9c5dffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.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/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc578b8121b06920648eadcec1563b.png)
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解题方法
4 . 已知抛物线
,点
,
在抛物线上,且横坐标分别为
,
,抛物线
上的点
在
,
之间(不包括点
,点
),过点
作直线
的垂线,垂足为
.
(1)求直线
斜率
的取值范围;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243f87cb3162c60372555b7a9b20fbe8.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/5743a3bf50e8146f519a7b4f32a958b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103070abee09399f1e9510a75c3ba9e8.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8025986143552af15445904eb6a64bf3.png)
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5 . 已知曲线
(
为参数)和曲线
(
为参数)相交于两点
,求两点
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d512e8dffd4f7ffcf5dabbb3c17d6328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e17311d701dad08582adf4a33408bc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
您最近一年使用:0次
名校
6 . 在平面直角坐标系内,已知点
及线段
,在线段
上任取一点
,线段
长度的最小值称为“点
到线段
的距离”,记为
.
(1)设点
,线段![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c037b199f33cbed1efcffdd2376d8c10.png)
,求
;
(2)设
,
,
,
,线段
,线段
,若点
满足
,求
关于
的函数解析式,并写出该函数的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fb005483a774d04231b2904c05a15d.png)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c037b199f33cbed1efcffdd2376d8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0951b050ecadf6f74a4b8e87018d577c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fb005483a774d04231b2904c05a15d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/8d7ff44b-28b2-4a4a-af5b-b4cb28e90b94.png?resizew=166)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4212e0f2da912518e8b02a741cc91ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b54b9cf95418bc3dce6e4c698b9907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733ca3719874892ee4ffbbaa2030b2f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32273ed59fcb3a5fbe0625ca9ee65ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9792659bdb65cc3136d1a96d8868fd3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b338a8c8993eaaaa53572fae7b97c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0ac51b04a8acc6d92656dd2daba0347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2018-01-02更新
|
487次组卷
|
4卷引用:上海市十二校2018届高三联考数学试题
上海市十二校2018届高三联考数学试题上海市实验学校2017-2018学年高三下学期第五次3月月考数学试题(已下线)专题18 直线和圆的方程(模拟练)-2新疆维吾尔自治区和田地区第二中学2022-2023学年高二上学期期中数学试题
7 . 在极坐标系中,点
,曲线
,以极点为坐标原点,极轴为
轴正半轴建立直角坐标系.
(1)在直角坐标系中,求点
的直角坐标及曲线
的参数方程;
(2)设点
为曲线
上的动点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ded6dd1c122d349fd14f8e71a8ffca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a602418116325402acbd0baedcd2550d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)在直角坐标系中,求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](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/eb167d4b98a95eeb37755d150aa826ee.png)
您最近一年使用:0次
2017-04-28更新
|
768次组卷
|
2卷引用:2017届广东深圳市高三第二次(4月)调研考试数学文试卷
名校
8 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bc24b06e0abd218044a27f597fa9e5.png)
.对于
,
,定义
与
之间的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a724e5071732f90d91d468389e8e956a.png)
.
(1)写出
中的所有元素,并求两元素间的距离的最大值;
(2)若集合
满足:
,且任意两元素间的距离均为2,求集合
中元素个数的最大值并写出此时的集合
;
(3)设集合
,
中有
个元素,记
中所有两元素间的距离的平均值为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bc24b06e0abd218044a27f597fa9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/855ce769f6795d1463744a0d74901fb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f0f12e1350ca9c2a81b6c36a840365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3bd6eccfd88084fd4b0c89c4c709d7f.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/a724e5071732f90d91d468389e8e956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3244bd0e909db80eb9e3ea79303b8351.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b626a2cad742c6613dc283fdab1e833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d7fa8a17135961c9c582f11d2e16cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1071ac8657ef1c4e1ea7e0530196298d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423cc16756424271a003917fbca775b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b67a5d723be5756086feeff090fe693.png)
您最近一年使用:0次
2017-04-06更新
|
958次组卷
|
2卷引用:2017届北京市石景山区高三3月统一练习数学理试卷
名校
9 . 已知圆
与圆
关于直线
对称,且点
在圆
上.
(1)判断圆
与圆
的位置关系;
(2)设
为圆
上任意一点,
,
三点不共线,
为
的平分线,且交
于
.求证:
与
的面积之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6435c32c37be871ac5979fef58a92d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599002fa5c20ea8f0f51f0c6df5c1ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)判断圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f18b56b270612d6fa696a5c1a76dfe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01225eca2322a6136314dedadcafa994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c965f16192e57a8079a40a0304ef339b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1269ea1057c555e256a8ea4a717e0f0.png)
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2016-12-04更新
|
610次组卷
|
4卷引用:2016届陕西省安康市高三第三次联考文科数学试卷
10 . 已知椭圆
的焦距为
,且经过点
.
(1)求椭圆E的方程;
(2)A是椭圆E与y轴正半轴的交点,椭圆E上是否存在两点M,N,使得△AMN是以A为直角顶点的等腰直角三角形?若存在,请说明有几个;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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆E的方程;
(2)A是椭圆E与y轴正半轴的交点,椭圆E上是否存在两点M,N,使得△AMN是以A为直角顶点的等腰直角三角形?若存在,请说明有几个;若不存在,请说明理由.
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