1 . 在平面直角坐标系
中,已知椭圆
的左、右焦点为
.
(1)若直线
与
轴相交于点
,
到直线
的距离为
,求
;
(2)若
,点
为椭圆
上的任意一点,设椭圆
的上、下顶点分别为
,记
的面积为
,
的面积为
,若
,求
的取值范围;
(3)若
,过点
的直线与椭圆交于
两点(
在
的上方),线段
上存在点
,使得
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3115e446aa63fabd996db9f5c39a7df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061af1c7a4480004221e253d813efe07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c10e33a64f5c35e60200b76524a5a83.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237c115d5b39d761e1cbcae031070b70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd8065fd9fe33e0b71d5933909f5c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808e0252f83af175e937db769f045a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddc18ef823feb3a4bf0737f3446f99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb0c703f6effcbcf1770569971b3cd2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df46b800478f98f9f7b4f4c51a90a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e42e19bb44c47d716c3c65034bf7aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593449de4253fc9f6f7e6a48a50d4a15.png)
您最近一年使用:0次
2 . 已知
、
,点
满足
.
(1)求点
的轨迹方程;
(2)记动点
轨迹为曲线
,直线
交曲线
于
、
两点,且以
为直径的圆过
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb17ca598f56fef3ce97d715d597d2c7.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)记动点
![](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/9e6e15daf7b14dbff32c390f4984dcfb.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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
,且点
在椭圆上.
的标准方程;
(2)如图,若一条斜率不为0的直线过点
与椭圆交于
两点,椭圆
的左、右顶点分别为
,直线
的斜率为
,直线
的斜率为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0e6f5ff0f4fa113f4cad9f72fbbcc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,若一条斜率不为0的直线过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.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/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07765d282ff61d422aba3fc5f0b61e2a.png)
您最近一年使用:0次
2024-02-01更新
|
2714次组卷
|
7卷引用:2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)云南省三校2024届高三高考备考实用性联考卷(五)数学试题湖南省长沙市雅礼中学2024届高三一模数学试卷云南省玉溪市第一中学2023-2024学年高二下学期3月月考数学试题(已下线)专题07 直线与圆、圆锥曲线江西省宜春市丰城市第九中学2023-2024学年高二下学期开学考试数学试题安徽省阜阳第一中学2023-2024学年高二下学期4月月考数学试题
名校
解题方法
4 . 已知点
为椭圆
的左焦点,
在C上.
(1)求C的方程;
(2)记(1)中轨迹为曲线C,在曲线C的上半部分取两点M,N,若
,
,且
.
①当
时,求四边形
的面积;
②求四边形
的面积最大时点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e1a85a657231ef717809d5a839ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2f483905437b31b8f60e2d388ec806.png)
(1)求C的方程;
(2)记(1)中轨迹为曲线C,在曲线C的上半部分取两点M,N,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e4a3aea4b4b0d87c014030a6ff9027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451fc6e4248b63e70595f23842f06c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe98ef73331666776210e74ea36555f8.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b032d78f28236864b69803022e442b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75bfa01c4013b4710a7fb71c305c0b7.png)
②求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75bfa01c4013b4710a7fb71c305c0b7.png)
您最近一年使用:0次
2024-01-22更新
|
567次组卷
|
3卷引用:2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)福建省厦门市厦门外国语学校2023-2024学年高二上学期期末模拟考试数学试题江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(二)
5 . 已知
为坐标原点,曲线
和曲线
有公共点,直线
与曲线
的左支相交于A,B两点,线段AB的中点为
.
(1)若曲线
和
有且仅有两个公共点,求曲线
的离心率;
(2)若
是曲线
上的点,且在第一象限,
,
是其左右焦点,当
为直角三角形时,求点
的横坐标;
(3)若直线
与曲线
相交于C、D两点,且直线OM经过线CD中点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f1bce3b41f0c0fd64043db71960761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10cb9214d8d79d857eaa0e7cfbc91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4211831377655be51acaf182280085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)若曲线
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266e3689cc366d5f0a7718ce9c20e818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e68bc07d048c7c7615b864883280d8.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆
,直线
.
(1)求证:对
,直线
与椭圆
总有两个不同交点;
(2)直线
与椭圆
交于
两点,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98592e0f2fbd50a18abf290254910a1.png)
(1)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b5544e6bbd816c45db57f740c5e8c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](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/483fb4cafaf60282217a6f2650e94b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-09更新
|
740次组卷
|
3卷引用:2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)重庆市黔江中学校2023-2024学年高二上学期11月考试数学试题江苏省南京市励志高级中学2023-2024学年高二上学期期末模拟数学试题
解题方法
7 . 已知椭圆
的离心率
,点
在
上,
为坐标原点.
(1)求
的标准方程;
(2)若不过原点
的直线
交
于
,
两点,
是线段
的中点,且直线
的斜率为2,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若不过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-02-14更新
|
1183次组卷
|
4卷引用:2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)1号卷·A10联盟2022-2023学年(2021级)高二上学期11月期中联考数学试卷(人教A版)1号卷·A10联盟2022-2023学年(2021级)高二上学期11月期中联考数学试卷(北师大版)云南省文山州广南县第十中学校2023-2024学年高二下学期3月月考数学试题
23-24高二上·上海·课后作业
8 . 已知直线
交椭圆
于点
、
,点
在此椭圆上运动.求点
到直线
的距离的最大值?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f524ac41ac7f7ee26b566bc145b082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
23-24高二上·上海·课后作业
解题方法
9 . 设直线与椭圆的方程分别为
与
,问
为何值时,
(1)直线与椭圆有一个公共点;
(2)直线与椭圆有两个公共点;
(3)直线与椭圆没有公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744ab5b95de8f2d9476b68158c445027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad31cc8c5973b7fb734a060bb25c608a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)直线与椭圆有一个公共点;
(2)直线与椭圆有两个公共点;
(3)直线与椭圆没有公共点.
您最近一年使用:0次
10 . 直线
被椭圆
所截得的弦长为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebb3b7f47e0decd48e64cb32aaa5903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b7c1422e9eead6d4aca39d77756afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d581ff306fe98572d894daaca3fcaa87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2023-09-11更新
|
977次组卷
|
6卷引用:2.2 椭圆
(已下线)2.2 椭圆(已下线)3.1.2 椭圆的几何性质(2)(已下线)第04讲 拓展一:直线与椭圆的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)专题05 椭圆及其性质(3大考点9种题型)(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(苏教版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10 椭圆的几何性质8种常见考法归类(2)