名校
解题方法
1 . 已知椭圆
的对称中心为坐标原点,对称轴为坐标轴,焦点在
轴上,离心率
,且过点
.
(1)求椭圆
的标准方程;
(2)若直线
与椭圆交于
两点,且直线
的倾斜角互补,判断直线
的斜率是否为定值?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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc1234aa2273bbae63aa9a3113e6620.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-09-29更新
|
1751次组卷
|
10卷引用:江西省上饶艺术学校2023-2024学年高二上学期10月月考数学试题
江西省上饶艺术学校2023-2024学年高二上学期10月月考数学试题四川省成都市蓉城名校联盟2023届高三上学期第一次联考文科数学试题宁夏银川市永宁县上游高级中学2023-2024学年高二上学期期中考试数学试题广东省韶关市北江实验学校2023-2024学年高二上学期10月月考数学试题福建省南平市浦城第一中学2023-2024学年高二上学期期中数学试题(已下线)考点19 解析几何中的探索性问题 2024届高考数学考点总动员(已下线)第三章 圆锥曲线的方程(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A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(分层练习)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第一册)(已下线)黄金卷04(已下线)专题10 椭圆的几何性质8种常见考法归类(2)
名校
解题方法
2 . 已知分别为椭圆
的左,右顶点,
为其右焦点,
,且点
在椭圆
上.
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba6af95c79e80c772653374c05c21f3.png)
您最近一年使用:0次
2023-05-07更新
|
1701次组卷
|
9卷引用:江西省丰城中学2023-2024学年高一上学期12月月考数学试题
江西省丰城中学2023-2024学年高一上学期12月月考数学试题广西桂林市、北海市2023届高三联合模拟考试数学(理)试题海南省琼海市2023届高三模拟考试数学试题四川省成都市双流区永安中学2022-2023学年高二下学期零模模拟考试数学试题湖南省长沙市明德中学2023-2024学年高三上学期入学考试数学试题(已下线)第02讲 3.1.2椭圆的简单几何性质(2)(已下线)第08讲 直线与圆锥曲线的位置关系(练习)(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)云南省昆明市2024届高三“三诊一模”摸底诊断测试数学试题变式题17-22
解题方法
3 . 已知椭圆
的焦距为
,左、右顶点分别为
,上顶点为B,且
.
(1)求椭圆C的方程;
(2)若过
且斜率为k的直线l与椭圆C在第一象限相交于点Q,与直线
相交于点P,与y轴相交于点M,且
.求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1735708848cfde06947647a29687a76.png)
(1)求椭圆C的方程;
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f69a7effc74ab83bd02bb4c2d9e9716.png)
您最近一年使用:0次
2023-04-23更新
|
306次组卷
|
3卷引用:江西省南昌市2023届高三二模数学(文)试题
名校
解题方法
4 . 已知椭圆C:
的离心率为
,短轴长为2.
(1)求椭圆C的方程;
(2)设O为坐标原点,F为椭圆C的右焦点,过F的直线l与C交于A,B两点,点M的坐标为
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆C的方程;
(2)设O为坐标原点,F为椭圆C的右焦点,过F的直线l与C交于A,B两点,点M的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57610afd116ab84660c807cc1aa3819.png)
您最近一年使用:0次
2023-08-17更新
|
1091次组卷
|
6卷引用:江西省南昌市第十中学2022-2023学年高二上学期期中数学试题
江西省南昌市第十中学2022-2023学年高二上学期期中数学试题江西省九江市永修县第一中学2023-2024学年高二上学期10月月考数学试题江西省上饶市余干县蓝天中学2023-2024学年高二上学期期中考试数学试题(已下线)2.4.2直线与圆锥曲线的综合问题(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)北京市第十一中学2023-2024学年高二上学期期中练习数学试题(已下线)专题08 椭圆双曲线综合大题(9题型)-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
名校
解题方法
5 . 已知椭圆
的离心率为
,焦距为4.
(1)求椭圆
的方程;
(2)设过椭圆的右焦点
的动直线
与椭圆交于
、
两点(点
在
轴上方),
、
为椭圆的左、右顶点,直线
,
与
轴分别交于点
、
,
为坐标原点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过椭圆的右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27b957de1bf137d15eb6321b4e58f1a.png)
您最近一年使用:0次
2023-02-26更新
|
563次组卷
|
4卷引用:江西省上饶市2023届高三第一次高考模拟考试数学(理)试题
江西省上饶市2023届高三第一次高考模拟考试数学(理)试题(已下线)江西省上饶市2023届高三第一次高考模拟考试数学(理)试题变式题16-20(已下线)专题16解析几何(解答题)四川省宜宾市南溪第一中学校2024届高三上学期一诊考试理科数学模拟试题
名校
解题方法
6 . 已知椭圆
,四个点
,
,
,
中恰有三点在椭圆C上.
(1)求椭圆C的方程;
(2)设直线
与椭圆C相交于A,B两点.若直线
与直线
的斜率的和为
,判断直线l是否经过定点,若过定点,求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f669a1d6376f795f05b47eb7d8067c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fbf46db1c38fdcefdfca8777a92875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea67de74c0d7a7c48df4329a625e9234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662c8324ff4c288337a2dbf78be863b4.png)
(1)求椭圆C的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e9f87f36df625060ebf7b0ede71b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3de68627f7f3d7f81b61bf743f311ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9019a986b3ba5fcefced99c566b5329c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
您最近一年使用:0次
2023-02-22更新
|
383次组卷
|
3卷引用:江西省南昌市第十九中学2022-2023学年高二下学期第一次(3月)月考数学试题
名校
解题方法
7 . 已知椭圆
:
的离心率为
,其左、右焦点分别为
、
,上顶点为
,且
.
(1)求椭圆
的方程;
(2)直线
:
与椭圆
交于
两点,О为坐标原点.试求当
为何值时,
恒为定值,并求此时
面积的最大值.
![](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/860884c0017c8bceb5b0edff796c144f.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/dc7a9140bf7ed15de4241aa9ad8924a4.png)
(1)求椭圆
![](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/d27bc3a7f511eb588c096c5672d5da49.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a0d9a2f14f7e789892487d6585804a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
2023-02-22更新
|
1092次组卷
|
5卷引用:江西省上饶市第一中学2022-2023学年高二下学期第一次月考(3月)数学试题
8 . 已知椭圆C:
,
,
为椭圆C的左、右顶点,
,
为左、右焦点,Q为椭圆C上任意一点.
(1)求直线
和
的斜率之积;
(2)直线l交椭圆C于点M,N两点(l不过点
),直线
与直线
的斜率分别是
,
且
,直线
和直线
交于点
.
①探究直线l是否过定点,若过定点求出该点坐标,若不过定点请说明理由;
②证明:
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3853a47e9138f78e83786b0d6e85bce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f387b16cc48e57112c89c8af2a90c1d6.png)
(2)直线l交椭圆C于点M,N两点(l不过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448eb7d301baa90fe59b05761830f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.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/78bb56032b37aaf40bfbac51f7fe2d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
①探究直线l是否过定点,若过定点求出该点坐标,若不过定点请说明理由;
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2023-02-15更新
|
801次组卷
|
4卷引用:江西省重点中学九江六校2022-2023学年高二上学期第一次联考数学试题
名校
解题方法
9 . 已知椭圆
:
(
),四点
,
,
,
中恰有三点在椭圆
上.
(1)求椭圆
的方程;
(2)设直线
不经过
点且与椭圆
相交于
,
两点,线段
的中点为
,若
,试问直线
是否经过定点?若经过定点,请求出定点坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/7b67c0525a41fffd3ff86fded5ce46c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa147625926cc1453cc20b42f0685a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c591b4f1df5b29cb3e03f136e376c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45213955caa6458ba08ee56153087489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d28e9672bc575bb3d5a9cb131084d2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-15更新
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1209次组卷
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5卷引用:江西省鹰潭市2023届高三二模数学试题(文科)
10 . 已知椭圆C:
的左、右顶点分别为A,B,右焦点为F,折线
与C交于M,N两点.
(1)当m=2时,求
的值;
(2)直线AM与BN交于点P,证明:点P在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/640bcaecb7b575307c199d828ba96384.png)
(1)当m=2时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3adfb8ef95245d7d073de76ceb053a.png)
(2)直线AM与BN交于点P,证明:点P在定直线上.
您最近一年使用:0次
2023-02-01更新
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481次组卷
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3卷引用:江西省宜春市宜丰县宜丰中学2023届高三上学期期末数学试题