名校
解题方法
1 . 已知圆锥曲线C的对称中心在原点,以坐标轴为对称轴,且经过点
与点
.
(1)求曲线C的方程;
(2)已知T为直线
上的动点(T不在x轴上),A,B为曲线C与x轴的交点,直线
与曲线C相交的另一点为M,直线
与曲线C相交的另一点为N,记
和
的面积分别为
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59a1d3e6a94f1bcea354d37318fd003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
(1)求曲线C的方程;
(2)已知T为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1ec05e3cec27677ded7b4aecaa62d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8059a935a2325a9e7abbcbf56aa167f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4aa8deeb53a8bf76532a4b3a1ca7ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615c4ead3a3e74c8ea748e1ac82a3672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2024-02-23更新
|
507次组卷
|
2卷引用:重庆市缙云教育联盟2024届高三下学期第二次诊断性检测数学试题
名校
解题方法
2 . 已知椭圆
的离心率为
,且过点
,点O为坐标原点.
(1)求椭圆C的方程;
(2)椭圆C上的动点M,P,Q满足直线
的斜率互为相反数,且点M不在坐标轴上,设直线
的斜率分别为
,求
的值.
![](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/1e501efaf72113fc8ee3d495004fa980.png)
(1)求椭圆C的方程;
(2)椭圆C上的动点M,P,Q满足直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592b4967f670b263ea9331370bc46940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df462d47fbca60c1321bc8fae66728dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2023-01-09更新
|
918次组卷
|
2卷引用:重庆市2023届高三第一次联合诊断【康德卷】数学试题
解题方法
3 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆
的标准方程;
(2)过点
的两条直线分别和椭圆
交于不同两点A,
(A,
异于点
且不关于坐标轴对称),直线
,
的斜率分别为
,
,且
.试问直线
是否恒过一定点?若是,求出该定点的坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6b94e42869013745050aba059b58dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d695d4b8eb4f37c2c1bf46a190d461a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333160ac2088b2f83ac1e0c446b5d8e1.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30c084de07c0c84de9348cfa688088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
4 . 已知
为坐标原点,点
在椭圆
上,椭圆
的左右焦点分别为
,且
.
(1)求椭圆
的标准方程;
(2)若点
在椭圆
上,原点
为
的重心,证明:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a7a78a0cb55d2396f7213432a86b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efbe4a54a27dc48e3f52d6249bd1681.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8629c9f5bf76510e77fad9d19ccaa4a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed4022e6522665dab4ce898a539e5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed4022e6522665dab4ce898a539e5c2.png)
您最近一年使用:0次
2022-01-23更新
|
2753次组卷
|
6卷引用:重庆市天星桥中学2022届高三上学期学业质量调研抽测(一)数学试题
名校
解题方法
5 . 已知椭圆
的焦距为
,且过点
.
(1)求
的标准方程;
(2)过
的右焦点的直线
与
交于
,
两点,
上一点
满足
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4212fe1dec12d82823a3e3fb5af826bb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](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/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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13bb1830508bfb5098310e67bbc77499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c19fa4cd646f4d877c3e58cc346651.png)
您最近一年使用:0次
2021-05-12更新
|
655次组卷
|
3卷引用:重庆市永川北山中学校2022届高三高考仿真数学试题
名校
解题方法
6 . 已知左、右焦点分别为
、
的椭圆C:
过点
,以
为直径的圆过C的下顶点A.
(1)求椭圆C的方程;
(2)若过点
的直线l与椭圆C相交于M,N两点,且直线
、
的斜率分别为
、
,证明:
为定值.
![](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/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558494a4594f69b0b679d8d588006efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
(1)求椭圆C的方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22840186db0afc0e2b2e8915ce79b998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2021-05-05更新
|
676次组卷
|
4卷引用:重庆市永川北山中学校2022届高三高考冲刺3数学试题
名校
解题方法
7 . 已知
为椭圆
上一点,
为坐标原点,
,
为椭圆
的左右焦点,若
,且
,
的面积为4,则该椭圆的标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/b920ecd63eb8f74aca15483064f01f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db30964618c3783c6d0c2358c06c4b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-09-19更新
|
1428次组卷
|
5卷引用:2020届重庆市第一中学高三下学期6月模拟数学(文)试题
2020届重庆市第一中学高三下学期6月模拟数学(文)试题(已下线)【南昌新东方】江西省南昌市外国语学校2020-2021学年高二上学期期中数学(理)试题18广东省广州市执信中学2020-2021学年高二上学期期中数学试题河南省许昌市建安区第一高级中学2023-2024学年高二上学期10月月考数学试题福建省泉州市德化县德化二中2023-2024学年高二上学期期中数学试题
名校
解题方法
8 . 已知椭圆C:
1(a>b>0)的左、右焦点分别为F1、F2,点P(﹣1,
)在椭圆C上,且|PF2|
.
(1)求椭圆C的方程;
(2)过点F2的直线l与椭圆C交于A,B两点,M为线段AB的中点,若椭圆C上存在点N,满足
3
(O为坐标原点),求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22ecb9b0a87ab5098571bdf80441231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a91116e174210063fd85491b4f8b63.png)
(1)求椭圆C的方程;
(2)过点F2的直线l与椭圆C交于A,B两点,M为线段AB的中点,若椭圆C上存在点N,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbafc2b76ab29a2ea3ae4daeba112680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e983303831a625870608ab6f7d9b6330.png)
您最近一年使用:0次
2020-06-29更新
|
1233次组卷
|
7卷引用:2020届重庆市高三5月调研(二诊)数学(文)试题
2020届重庆市高三5月调研(二诊)数学(文)试题天津市和平区2022届高三下学期一模数学试题(已下线)专题19 圆锥曲线综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题19 圆锥曲线综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)天津市第二南开学校2022-2023学年高三下学期开学学情调查数学试题天津市耀华中学2024届高三上学期暑期学情反馈数学试题天津市河东区第四十五中学2024届高三上学期12月月考数学试题
名校
9 . 已知椭圆
两焦点坐标分别为
,且经过点
.
(1)求椭圆
的标准方程;
(2)已知点
,直线
与椭圆
交于
、
两点,若
是以
为直角顶点的等腰直角三角形,求所有满足条件的直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871868260c78a20767eae39bcdb97476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a7a78a0cb55d2396f7213432a86b86.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6cffa52177f31cd10c42d00f69d4da1.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a9fc2dda89829fa2c610a8fce86d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-02-21更新
|
240次组卷
|
3卷引用:2019届重庆市合川瑞山中学高三下学期模拟训练(文)数学试题
2014·重庆·一模
名校
解题方法
10 . 已知椭圆
:
和椭圆
:
的离心率相同,且点
在椭圆
上.
(1)求椭圆
的方程;
(2)设
为椭圆
上一点,过点
作直线交椭圆
于
,
两点,且
恰为弦
的中点,则当点
变化时,试问
的面积是否为常数,若是,求出此常数,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8da36e3081bfe5d32c9ec70be4da3da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf9680f74a9ac5d934304654ce2771.png)
您最近一年使用:0次
2020-11-12更新
|
231次组卷
|
6卷引用:2014届重庆市高三下学期考前模拟(二诊)理科数学试卷