名校
1 . 已知椭圆
的离心率为
,椭圆的中心
到直线
的距离为
.
(1)求椭圆
的方程;
(2)设过椭圆
的右焦点
且斜率为
的直线
和椭圆交于
两点,对于椭圆
上任意一点
,若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dccdc4f73b409dae07a0661a4281ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa82a15632a545ce2cc6dc998899807.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆
![](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/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54bb99e14a2c48a600569891cb838069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adebff9fb726cd58eda1ef994890901.png)
您最近一年使用:0次
2022-04-04更新
|
620次组卷
|
2卷引用:江西省八所重点中学2022届高三4月联考数学(文)试题
名校
解题方法
2 . 已知椭圆
的左、右顶点分别为
,上顶点为
,且
.
(1)求椭圆
的标准方程;
(2)点
,
为坐标原点,
为椭圆
上的两个动点,线段
的中点在直线
上,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4cc7e0652c566671737795b156a8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb94909e86f4bad31e80f7e42ac514f8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efa0031095d2186f68e407859eb37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
您最近一年使用:0次
2022-04-03更新
|
459次组卷
|
2卷引用:江西省萍乡市2022届高三上学期期末考试数学(文)试题
3 . 已知椭圆
过点
,且
的上顶点到右顶点的距离为
.
(1)求
的方程;
(2)若点
都在
上,直线PQ不与
轴垂直,原点
恰好是
的重心,且点
到PQ的距离为
,求PQ的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96111d6c3d03db7ef98420039f64c20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea33baec6ac30ceb415e74dfbeef569a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fc107c4b33d6dd648b396156494ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
您最近一年使用:0次
名校
4 . 已知椭圆E:
的离心率为
,P为椭圆E上一点,Q为圆
上一点,
的最大值为3(P,Q异于椭圆E的上下顶点).
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946135755153408/2947907200778240/STEM/6ad34a35-8bea-452e-8287-4e3794171077.png?resizew=224)
(1)求椭圆E的方程;
(2)A为椭圆E的下顶点,直线AP,AQ的科率分别记为
,
,且
,求证:
APQ为直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82358b724051b032c7ec734a226ae84.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946135755153408/2947907200778240/STEM/6ad34a35-8bea-452e-8287-4e3794171077.png?resizew=224)
(1)求椭圆E的方程;
(2)A为椭圆E的下顶点,直线AP,AQ的科率分别记为
![](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/a0aea8e4a6e524f43f9a13c1ef4fbddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
您最近一年使用:0次
2022-03-31更新
|
957次组卷
|
3卷引用:江西省九江市2022届第二次高考模拟统一考试数学( 文)试题
解题方法
5 . 已知椭圆
的离心率为
,P为椭圆E上一点,Q为圆
上一点,
的最大值为3(P,Q异于椭圆E的上下顶点).
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946077197844480/2947290699497472/STEM/64b4427d51904c5592c7e6c5ed2b4bc1.png?resizew=231)
(1)求椭圆E的方程;
(2)A为椭圆E的下顶点,直线AP,AQ的斜率分别记为
,
,且
,求证:直线PQ过定点,并求出此定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://img.xkw.com/dksih/QBM/2022/3/28/2946077197844480/2947290699497472/STEM/64b4427d51904c5592c7e6c5ed2b4bc1.png?resizew=231)
(1)求椭圆E的方程;
(2)A为椭圆E的下顶点,直线AP,AQ的斜率分别记为
![](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/a0aea8e4a6e524f43f9a13c1ef4fbddd.png)
您最近一年使用:0次
解题方法
6 . 设椭圆
,点
,
为E的左、右焦点,椭圆的离心率
,点
在椭圆E上.
(1)求椭圆E的方程;
(2)M是直线
上任意一点,过M作椭圆E的两条切线MA,MB,(A,B为切点).
①求证:
;
②求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.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/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
(1)求椭圆E的方程;
(2)M是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df9b3123b0fc113661918d258aa39e.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
您最近一年使用:0次
2022-03-22更新
|
745次组卷
|
2卷引用:江西省南昌市第二中学等十五所名校2022届高三下学期第一次模拟考数学(理)试题
名校
7 . 已知椭圆
的左、右焦点分别为
,
,离心率为
,点A在椭圆C上,
,
,过
与坐标轴不垂直的直线l与椭圆C交于P,Q两点,N为线段PQ的中点.
(1)求椭圆C的方程;
(2)已知点
,且
,求线段MN所在的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee6b72b95a4296f256e2bc1db9997e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5501e5af18cf5c9ec3b7cb0884fea1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求椭圆C的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3cf6fa06aa281a55a991a80b1559e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8c957b71beace01e35905eccbca90d.png)
您最近一年使用:0次
2022-03-22更新
|
414次组卷
|
4卷引用:江西省宜春市铜鼓中学2021-2022学年高二下学期第一次月考非实验班数学(文)试题
江西省宜春市铜鼓中学2021-2022学年高二下学期第一次月考非实验班数学(文)试题江西省赣州市教育发展联盟2021-2022学年高二下学期第8次联考数学(文)试题黑龙江省齐齐哈尔市第八中学2021-2022学年高二下学期开学考试数学试题(已下线)北京市海淀区2023届高三上学期期末练习数学试题变式题16-21
8 . 在平面直角坐标系
中,
,
,
,
,点P是平面内的动点.若以
为直径的圆O与以
为直径的圆T内切.
(1)证明:
为定值,并求点P的轨迹E的方程;
(2)设斜率为
的直线l与曲线E相交于C、D两点,问在E上是否存在一点Q,使直线
、
与y轴所围成的三角形是底边在y轴上的等腰三角形?若存在,求出点Q的横坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/e1cf8af6e62058cc4e2d83d5da7f4c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f36374ce95a4945d0e58264c2b271f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1b3031d7393a63719166285314d73f.png)
(2)设斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c118858379800688c993a8b61270b356.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆
:
的左、右焦点分别为
,
,点
在椭圆
上,满足
,且
面积的最大值为
.
(1)求椭圆
的方程;
(2)点
,点A,B在椭圆
上,点N在直线
:
,满足
,
,试问
是否为定值?若是,求出该定值,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f595683f69d5d6b5ca76408b0ff6ff17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdcfc71b422a73d7110b17e57c0e161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091c83390d0755e1b72755cf37490351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770df925dc6286c73505a5e51f98d6b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45996655edb44a3123bc97663ca28a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
您最近一年使用:0次
10 . 已知椭圆
过点
.
(1)求C的标准方程;
(2)若过点
且不与x轴垂直的直线
与C交于
两点,记C的上顶点为D,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4a6c4a511060116fbfc081dbd12e60.png)
(1)求C的标准方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23a9301fc1ac223f9ddee3e918b4d882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0133b26e390fe11bc46a35e6b523b809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd28cdb9f395d0506a50286f55f866d1.png)
您最近一年使用:0次
2022-03-15更新
|
225次组卷
|
2卷引用:江西省2022届高三智慧上进大联考一轮复习验收数学(文)试题