名校
解题方法
1 . 已知椭圆
的左、右焦点分别为
,
,且过点
.
(1)求椭圆E的标准方程;
(2)过椭圆E的左焦点
的直线与椭圆E交于A,B两点,求
的面积最大时直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4a7482cb81b34df5a11807b8136a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cfc83cab6cd17842f28b9c37836673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a7a78a0cb55d2396f7213432a86b86.png)
(1)求椭圆E的标准方程;
(2)过椭圆E的左焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9360ec6a0fc1e5be5caeec35f4645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8376a8a3dd42eaa0558501a3e2a2bdb4.png)
您最近一年使用:0次
2023-01-08更新
|
321次组卷
|
2卷引用:四川省成都市蓉城高中联盟2022-2023学年高二上期期末考试数学(文科)试题
2 . 已知椭圆
过点
和
.
(1)求椭圆
的方程;
(2)过点
作直线
交椭圆
于不同的两点
,直线
交
轴于点
,直线
交
轴于点
.若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f40d5459e1385ab7d829ea96ca0b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f31a7cd8add5a5589c54b3d5412dde8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4effc718edc9ada7580cb3a4019fc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/bd33764ff4efddfe11a98a609753715c.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/d2be49c37e30a3ced0364c3e74d8c687.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/2f1bf8f6237edc726337428f19282b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
3 . 已知椭圆
过点
,
两点.
(1)求椭圆E的方程;
(2)过点P的直线l与椭圆E交于C,D两点.
(i)若点P坐标为
,直线BC,BD分别与x轴交于M,N两点.求证:
;
(ii)若点P坐标为
,直线g的方程为
,椭圆E上存在定点Q,使直线QC,QD分别与直线g交于M,N两点,且
.请直接写出点Q的坐标,结论不需证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
(1)求椭圆E的方程;
(2)过点P的直线l与椭圆E交于C,D两点.
(i)若点P坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b485b62d004d52fb31d6ed99ccb7669.png)
(ii)若点P坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8ba2b1920103e0879cff3de727a90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/382b0ad2e5ba2ddd25654b64eafce84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b485b62d004d52fb31d6ed99ccb7669.png)
您最近一年使用:0次
解题方法
4 . 已知椭圆
的左右焦点分别是
,左右顶点分别是
.
(1)若椭圆
上的点
到
两点的距离之和等于4,求此椭圆
的方程;
(2)若
是椭圆
上异于
的任一点,记直线
与
的斜率分别为
,且
,试求椭圆
的离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7638c88f01d609d79947033ed4ff36a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67baac84cf5c95d06d50c36cab7c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42be0cf19dd95496f0ce52f72cd10f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151e09f3a383d7811c619eef3a6398cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(
)上一点,
,
是
的焦点,
.
(1)若
,求椭圆
的离心率;
(2)若点
的坐标为
,求椭圆
的标准方程.
![](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/f3dc5620627d34073f8de07147187a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6adab224b9e3552b032249e6149671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cceff0e7d103475c3ba9a2712f373185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2023-01-03更新
|
485次组卷
|
3卷引用:广东省深圳市龙华区2021-2022学年高二上学期期末数学试题
6 . 已知椭圆
的离心率为
,且经过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/89a0acd9-b7fb-4dd3-ac32-5d5232965431.jpg?resizew=179)
(1)求椭圆
的方程;
(2)若直线
与椭圆
交于
两点,
为坐标原点,直线
的斜率之积等于
,试探求
的面积是否为定值,并说明理由.
![](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/480f004c98a0df86a35a48bc973f0472.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/89a0acd9-b7fb-4dd3-ac32-5d5232965431.jpg?resizew=179)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091145fcc157587a3fc8e0b7c7c0ecb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2022-12-29更新
|
845次组卷
|
4卷引用:山东省淄博市淄博第五中学2022-2023学年高二上学期期末数学试题
解题方法
7 . 设椭圆E:
(
)的左、右焦点分别为
,
,点
在椭圆E上.
(1)求椭圆E的方程;
(2)设点T在直线
上,过T的两条直线分别交E于A,B两点和P,Q两点,且
,求直线
的斜率与直线
的斜率之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/93942c01c84441f20e269d9173c4ec11.png)
(1)求椭圆E的方程;
(2)设点T在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79f9972cd4f14ecfcea79f005800fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2022-12-27更新
|
709次组卷
|
4卷引用:河北省保定市2023届高三上学期期末数学试题
河北省保定市2023届高三上学期期末数学试题江苏省南通市2022-2023学年高三上学期12月调研测试数学试题(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(已下线)第五篇 向量与几何 专题5 调和点列 微点4 调和点列综合训练
名校
解题方法
8 . 已知
分别是椭圆
的左、右焦点,椭圆C过
和
两点,点P在线段
上,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b54b9cf95418bc3dce6e4c698b9907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34005d3b709a89e3db6bb786bbfb2369.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-12-24更新
|
1255次组卷
|
9卷引用:四川省成都市树德中学2022-2023学年高二上学期期末检测数学(文)试题
四川省成都市树德中学2022-2023学年高二上学期期末检测数学(文)试题云南省昆明市东川明月中学(原东川区高级中学)2022-2023学年高二上学期期末考试数学试题新疆泽普县第二中学2022-2023学年高二上学期期末考试数学试题江西省赣州市九校2023届高三上学期12月质量检测数学(理)试题江西省赣州市九校2023届高三上学期12月质量检测数学(文)试题河南省部分学校2022-2023学年高三12月大联考文科数学试题河南省部分学校2022-2023学年高三12月大联考理科数学试题安徽师范大学附属中学2023届高三上学期1月月考数学试题(已下线)第五节 椭圆 第一课时 椭圆的定义、方程与性质 A素养养成卷
22-23高三上·北京·阶段练习
9 . 已知椭圆
的焦点为
,
,且经过点
.
(1)求椭圆
的标准方程;
(2)直线
:
与曲线
交于
,
两点,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/e97b622024e4fe8348bf327f62f3a6ab.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aeabebd5bd9968bf5604ae1243476b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/c482f270b5d1961f03d5a58c9912867c.png)
您最近一年使用:0次
名校
解题方法
10 . 已知圆
与椭圆
相交于点
,
且椭圆的离心率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08596ab7ad94031331c93db6f9ec549.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/64bf5edf-5c24-4715-bc6b-719459c360d9.png?resizew=238)
(1)求r的值和椭圆C的方程;
(2)过M点的直线l交圆O和椭圆C分别于
两点.
①若
,求直线l的方程;
②设直线MA的斜率为k,直线NA的斜率为
,过M点斜率为
的直线交椭圆C于异于M的P点,若
,则直线PB是否过定点,如果过定点,求出定点坐标,如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3285a2383fa18025034cf9876175295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25e326fdf9e5456f48e8a99a069f379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d269b408e9993d393f93947bb00063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08596ab7ad94031331c93db6f9ec549.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/64bf5edf-5c24-4715-bc6b-719459c360d9.png?resizew=238)
(1)求r的值和椭圆C的方程;
(2)过M点的直线l交圆O和椭圆C分别于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378ffd5d3745d578308e1f154600e51d.png)
②设直线MA的斜率为k,直线NA的斜率为
![](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