1 . 已知椭圆C:
的焦距为
,且过点
.
(1)求椭圆C的方程;
(2)设与坐标轴不垂直的直线l交椭圆C于M,N两点(异于椭圆顶点),点P为线段MN的中点,
为坐标原点.
①若点P在直线
上,求证:线段
的垂直平分线恒过定点
,并求出点
的坐标;
②求证:当
的面积最大时,直线OM与ON的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
(1)求椭圆C的方程;
(2)设与坐标轴不垂直的直线l交椭圆C于M,N两点(异于椭圆顶点),点P为线段MN的中点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①若点P在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
②求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
2023-05-25更新
|
885次组卷
|
3卷引用:上海市格致中学2023届高三三模数学试题
解题方法
2 . 已知椭圆
的左、右焦点分别为
,
,离心率
,
为椭圆上一动点,
面积的最大值为
.
(1)求椭圆
的标准方程;
(2)设点
为椭圆
与
轴负半轴的交点,不过点
且不垂直于坐标轴的直线
交椭圆
于S,
两点,直线NS,NT分别与
轴交于C,D两点,若C,D的横坐标之积是2.问:直线
是否过定点?如果是,求出定点坐标,如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.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/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
3 . 已知椭圆
的离心率为
,上顶点的坐标为
,
(1)求椭圆C的方程.
(2)若椭圆C下顶点是B,M是C上一点(不与A,B重合),直线AM与直线
交于点P,直线BP交椭圆C于点N.求证:直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
(1)求椭圆C的方程.
(2)若椭圆C下顶点是B,M是C上一点(不与A,B重合),直线AM与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆C:
,直线l与椭圆C交于A,B两点.
(1)点
为椭圆C上的动点(与点A,B不重合),若直线PA,直线PB的斜率存在且斜率之积为
,试探究直线l是否过定点,并说明理由;
(2)若
.过点O作
,垂足为点Q,求点Q的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c9e6d4506b9ac289a1aa6c83c6127e.png)
您最近一年使用:0次
5 . 已知椭圆
:
的长轴为双曲线
的实轴,且椭圆
过点
.
(1)求椭圆
的标准方程;
(2)点
、
是椭圆
上异于点
的两个不同的点,直线
与
的斜率均存在,分别记为
,
,且
,求证:直线
恒过定点,并求出定点的坐标.
![](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/28675c5bcb91f9084684c58095f37ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/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/151e09f3a383d7811c619eef3a6398cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-09-22更新
|
1354次组卷
|
6卷引用:山东省淄博实验中学、淄博齐盛高中2022-2023学年高二上学期11月第一次模块考试数学试题
山东省淄博实验中学、淄博齐盛高中2022-2023学年高二上学期11月第一次模块考试数学试题(已下线)重难专攻(十)圆锥曲线中的定点问题 A卷素养养成卷(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)第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)(已下线)3.2.2 双曲线的几何性质(3)四川省成都市成华区某校2023-2024学年高三“三诊”数学(文)试题
名校
解题方法
6 . 已知椭圆
的焦点分别
别为
的上、下顶点,过
且垂直于
的直线与
交于
两点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f5450c5a61b856800ea36d48406f12.png)
(1)求椭圆
的方程;
(2)已知原点
,过
的直线
分别交
于
两点和
两点,
在
轴的上方,若
三点共线,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa0ee1b69fd4cf29667651bf645b441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f5450c5a61b856800ea36d48406f12.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedd56a6be4b56acdf712775ec4f2dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
您最近一年使用:0次
解题方法
7 . 已知椭圆:
的离心率为
,
、
分别是其左、右焦点,若
是椭圆上的右顶点,且
.
(1)求椭圆的方程;
(2)设直线
与椭圆交于
两点,点
关于
轴的对称点为
(
与
不重合),问直线
与
轴是否交于一个定点?若是,请写出该定点的坐标,并证明你的结论;若不是,请说明理由.
![](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/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/30eb4ec2d2c015bfaa0da0c1bad4b799.png)
(1)求椭圆的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e01f73745160df8ad3683f89a50ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2023-04-26更新
|
959次组卷
|
6卷引用:四川省德阳市2023届高三下学期4月三诊考试理科数学试题
解题方法
8 . 已知椭圆
的长轴长为4,A,B是其左、右顶点,M是椭圆上异于A,B的动点,且
.
(1)求椭圆C的方程;
(2)若P为直线
上一点,PA,PB分别与椭圆交于C,D两点.
①证明:直线CD过椭圆右焦点
;
②椭圆的左焦点为
,求
的周长是否为定值,若是,求出该定值,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e870d323a62a728a87efd0d58a6604.png)
(1)求椭圆C的方程;
(2)若P为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
①证明:直线CD过椭圆右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
②椭圆的左焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe9ac6c866f9b2fd2eca32a5da2c298.png)
您最近一年使用:0次
2023-04-16更新
|
900次组卷
|
6卷引用:甘肃省2023届高三二模文科数学试题
甘肃省2023届高三二模文科数学试题甘肃省武威市凉州区2023届高三下学期第四次诊断考试数学(文)试题(已下线)数学(全国甲卷文科)(已下线)专题15解析几何(解答题)四川省成都市简阳市阳安中学2023届高三模拟训练(一)数学(文科)试题甘肃省2023届高三第二次诊断文科数学试题
名校
解题方法
9 . 已知椭圆
的离心率是
,
是椭圆C上一点.
(1)求椭圆C的标准方程;
(2)过点
的直线l与椭圆C交于A,B(异于点P)两点,直线PA,PB的斜率分别是
,
,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/d2bd2bb1af2896920f53ae5b670dd4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
(1)求椭圆C的标准方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa0b70d8d31f7be38e1936242fedddb.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/b4757181824e15e0f21e5bdd55448783.png)
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2023-04-15更新
|
1064次组卷
|
8卷引用:辽宁省部分学校联考2022-2023学年高二下学期4月月考数学试题
解题方法
10 . 已知动点
到点
的距离与到直线
的距离之比为
,设动点
的轨迹为曲线
.
(1)求
的方程;
(2)若直线
与曲线
交于
两点,且直线
(
为坐标原点)的斜率
满足
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c7b07ace87ed58fdc1f1bc78a04aeda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ace82d9a163e2dc42dc5ab45746b10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448f5c45be5e4ee2e189204d334b83fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a823f4424888eb5e03eec94f60da589.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/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4dceb351e0c4833fac917bf54f0b605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次