名校
解题方法
1 . 已知椭圆
的离心率为
,点
在
上,
的长轴长为
.
(1)求
的方程;
(2)已知原点为
,点
在
上,
的中点为
,过点
的直线与
交于点
,且线段
恰好被点
平分,判断
是否为定值?若为定值,求出该定值;若不为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d01bbdcc25ec5eedb21c14c82fa6ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8806602a7954aa6a067d8c6aed8e239f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知原点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834a37be1f8a4100c7bbc5972cca1e89.png)
您最近一年使用:0次
2024-03-07更新
|
488次组卷
|
3卷引用:内蒙古自治区赤峰市松山外国语学校2024届高三下学期开学考试数学(理)试题
解题方法
2 . 已知椭圆
的短半轴长
,且椭圆上一点与椭圆的两个焦点构成的三角形的周长为
.
(1)求椭圆
的方程;
(2)设直线
与椭圆
交于
,
两点,若以
为直径的圆经过椭圆的右顶点
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3643fa70165ed9fef1398bc9443e7a02.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a49c27746887c299cd3f5f6b0ce8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
3 . 已知椭圆
经过点
,离心率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆的方程;
(2)斜率为
的直线
不经过点
,且与椭圆相交于
两点,直线
和直线
的斜率分别记为
,
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bea681006f614f8a070e9c6a942c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆的方程;
(2)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.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/83d200a411fbc2f50ad72f1fd729a7d7.png)
您最近一年使用:0次
4 . 已知椭圆
的离心率为
,且椭圆上一点与椭圆两个焦点构成的三角形的周长为
,
(1)求椭圆
的方程.
(2)设直线
与椭圆交于
两点,若以
为直径的圆经过椭圆的右顶点
,求
的值及
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c14ff9b66f21c05e52dc3c8908c2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3643fa70165ed9fef1398bc9443e7a02.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf46f98449e6b3cd06d129d003ae32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
5 . 在平面直角坐标系
中,点A,B分别在x轴,y轴上运动,且
,动点P满足
.
(1)求动点P的轨迹C的方程;
(2)设点M,N在曲线C上,O为坐标原点,设直线
,
的斜率分别为
,
,且
,试判断
的面积是否为定值?若为定值,求出该定值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b4836786aca156de325464ea2ecd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee4dbf8d1be07b2f95ac0d26a9262f9.png)
(1)求动点P的轨迹C的方程;
(2)设点M,N在曲线C上,O为坐标原点,设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.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/02324abee955451054237a932230500a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
您最近一年使用:0次
2024-01-14更新
|
897次组卷
|
5卷引用:内蒙古自治区呼和浩特市剑桥中学2023-2024学年高二下学期第一次(3月)月考数学试题
内蒙古自治区呼和浩特市剑桥中学2023-2024学年高二下学期第一次(3月)月考数学试题陕西省宝鸡市2024届高三上学期高考模拟检测(一)数学(理)试题重庆市九龙坡区重庆实验外国语学校2024届高三下学期入学测试数学试题(已下线)专题06 直线与圆、椭圆方程(分层练)(三大题型+12道精选真题)宁夏银川市第二中学2024届高三第一次模拟考试数学(理)试题
6 . 已知圆
为圆
上的点,过点
作
轴于点
,点
是直线
上一点,且满足
.
(1)求点
的轨迹
的方程;
(2)设
分别为轨迹
与
轴的左、右交点,
是轨迹
上不同于
的动点,直线
,
与直线
分别交于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dad1c2707ac8e2715465af33926db09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66bf4538a775c075e2a1e4b1b9e2402f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb0cb4b2e0a7af501779001e4f6bb6c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26389703c40a3c2eac927e372858709.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
解题方法
7 . 已知椭圆
,离心率
,过点
.
(1)求
的方程;
(2)直线
过点
,交椭圆于
、
两点,记
,并设直线
、直线
的斜率分别为
、
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
(1)求
![](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/b25e326fdf9e5456f48e8a99a069f379.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/74c92e835e6811cdf63caf16ed19af9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c023f4b501684abd869b36d6e6c7f21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb6ce4b2e186bae81b561b4d958e9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18abc8b447e4a6ff19e6bd4a30cb7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bd042cab64ba961e54d75f69d12dcf.png)
您最近一年使用:0次
8 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
离心率等于
且椭圆C经过点
.
(1)求椭圆的标准方程
;
(2)若直线
与轨迹
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/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c2f5ccd9d7faa3f6027f89758e7b05.png)
(1)求椭圆的标准方程
![](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/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d8d57d44169246811fb5ed7e55c6b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2023-11-10更新
|
2073次组卷
|
6卷引用:内蒙古蒙东七校2024届高三上学期11月联考数学(文)试题
名校
解题方法
9 . 已知椭圆
的左、右焦点为
,
,离心率为
.点P是椭圆C上不同于顶点的任意一点,射线
、
分别与椭圆C交于点A、B,
的周长为8.
(1)求椭圆C的标准方程;
(2)若
,
,求证:
为定值.
![](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/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8144da365530cc0560de2d4946c96a1d.png)
(1)求椭圆C的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678764669f89f7f7c1e2f986b642b466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5749effb19c4a35500b1b1162e33c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
您最近一年使用:0次
2023-09-30更新
|
2618次组卷
|
12卷引用:内蒙古赤峰二中2023-2024学年高三上学期第二次月考理科数学试题
内蒙古赤峰二中2023-2024学年高三上学期第二次月考理科数学试题四川省南充高级中学2022-2023学年高三下学期第三次模拟数学文科试题(已下线)单元提升卷10 平面解析几何(已下线)阶段性检测4.1(易)(范围:高考全部内容)(已下线)模块四 专题6 大题分类练(圆锥曲线的方程)拔高能力练(人教A)(已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员【练】安徽省安庆市桐城市桐城中学2023-2024学年高二上学期第二次教学质量检测数学试题(已下线)专题3-2 椭圆大题综合11种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)(已下线)第八章 解析几何综合测试B(提升卷)(已下线)专题23 椭圆的简单几何性质10种常见考法归类(3)(已下线)专题10 椭圆的几何性质8种常见考法归类(2)江西省南昌市第十九中学2024届高三上学期11月期中考试数学试题
名校
解题方法
10 . 已知椭圆C:
过点
,且C的右焦点为
.
(1)求C的离心率;
(2)过点F且斜率为1的直线与C交于M,N两点,P直线
上的动点,记直线PM,PN,PF的斜率分别为
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
(1)求C的离心率;
(2)过点F且斜率为1的直线与C交于M,N两点,P直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224d30ca84f1aeeeda7a718e751a4925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1456e81321ccb20077b34562ca9cffbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090b7ee52d644d0c630ef44aec1726dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491223c784a273eaa0ca6323632bc248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3db99727bf6c3f93753d572d31067cf7.png)
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2023-09-10更新
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7卷引用:内蒙古赤峰市赤峰二中2024届高三上学期第三次月考数学(文)试题
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