名校
解题方法
1 . 已知
,
分别为椭圆
的左、右焦点,焦距为2,
,
分别为椭圆C的上、下顶点,椭圆C的右顶点为A,直线
,
的斜率之积为
.
(1)求椭圆C的标准方程;
(2)设过右顶点A的直线
与C交于另外一点B,与
垂直的直线
与
交于点M,与y轴交于点N;若
,且
(O为坐标原点),求直线
的斜率.
![](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/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b93e3f4eb68d7e137c034d9d32094be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8671e4ccb0d0da8b6cf19b0669fe76d9.png)
(1)求椭圆C的标准方程;
(2)设过右顶点A的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ded51ed307a019fb209cf5fa31bed4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8928625ad6575b6ce7545178005b59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
名校
解题方法
2 . 在平面直角坐标系xOy中,椭圆
的左焦点为点F,离心率为
,过点F且与x轴垂直的直线被椭圆截得的线段长为3.
(1)求椭圆C的方程;
(2)设不过原点O且斜率为
的直线l与椭圆C交于不同的两点P,Q,线段PQ的中点为T,直线OT与椭圆C交于两点M,N,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆C的方程;
(2)设不过原点O且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20553e0b4f149dd34c3623676149d43.png)
您最近一年使用:0次
2024-03-25更新
|
933次组卷
|
2卷引用:天津和平区2024届高三一模数学试题
解题方法
3 . 设椭圆
的右顶点为
,上顶点为
.已知椭圆的离心率为
,
.
(1)求椭圆的方程;
(2)设直线
与椭圆交于
,
两点,
与直线
交于点
,且点
,
均在第四象限.若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b685dfb277b4d68a4c390152339898e.png)
(1)求椭圆的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b408a02331b54b3286d0eefb29908ee2.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/0f85fca60a11e1af2bf50138d0e3fe62.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35128bd3771c59cd37c49f6d2b8799d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
4 . 已知椭圆
的离心率为
,椭圆的一个顶点与两个焦点构成的三角形面积为2. 已知直线
与椭圆C交于A,B两点,且与x轴,y轴交于M,N两点.
(1)求椭圆C的标准方程;
(2)若
,求k的值;
(3)若点Q的坐标为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53112fe62f62d23cc1f982099f0b0acc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/7a11261c-c492-4346-aef5-d3884c920ed8.png?resizew=175)
(1)求椭圆C的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5df68b7d1fd358239f30ab81fd6014.png)
(3)若点Q的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174ce6907c1d4b19c59ac3a35188a3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d871b0b46194d7300950e04f085533d2.png)
您最近一年使用:0次
2023-12-25更新
|
1301次组卷
|
10卷引用:【全国市级联考】天津市部分区2018年高三质量调查(二)数学(文)试题
【全国市级联考】天津市部分区2018年高三质量调查(二)数学(文)试题(已下线)专题44 盘点圆锥曲线中的定值问题——备战2022年高考数学二轮复习常考点专题突破上海交通大学附属中学2023届高三下学期期中数学试题(已下线)重难点突破16 圆锥曲线中的定点、定值问题 (十大题型)-1上海市浦东新区进才中学2023-2024学年高二上学期12月月考数学试题广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(一)宁夏银川市宁夏育才中学2023-2024学年高三上学期月考五数学(理科)试卷上海市新川中学2023-2024学年高二上学期期末数学试题上海市嘉定区第二中学2023-2024学年高二下学期3月月考数学试题广西壮族自治区百色市德保县德保高中2023-2024学年高二下学期3月月考数学试题
解题方法
5 . 在平面直角坐标系
中,已知椭圆
与椭圆
,且椭圆
过椭圆
的焦点.过点
的直线l与椭圆
交于A,B两点,与椭圆
交于C,D两点.
(1)求椭圆
的标准方程;
(2)若存在斜率不为0的直线l,使得
,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2486f6f0c37ffc30cf7f45fcdaf09623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7956018da8a5d497474123179e70cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d466e7019fc215699264d18069b87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若存在斜率不为0的直线l,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f62d8393c3fd719f850a588c81daebe.png)
您最近一年使用:0次
6 . 已知椭圆
:
(
)的右焦点为
,短轴长是长轴长的
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/26/38ada9f9-13d5-4d20-9ac4-183e0fc8c3ac.png?resizew=207)
(1)求椭圆的方程;
(2)
是椭圆
上的动点,过点
作椭圆
的切线
,
与直线
交于点
,若
(
为坐标原点)的面积为
,求点
的坐标.
![](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/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/26/38ada9f9-13d5-4d20-9ac4-183e0fc8c3ac.png?resizew=207)
(1)求椭圆的方程;
(2)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc02f00cf00a6dfd88b53a90f1f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04702611fa1d3e01a4fc93e1c5cc6a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2023-03-23更新
|
772次组卷
|
4卷引用:天津市和平区耀华中学2024届高三上学期期末数学试题
天津市和平区耀华中学2024届高三上学期期末数学试题甘肃省定西市2022-2023学年高三下学期教学质量检测考试理科数学试题(已下线)专题16解析几何(解答题)(已下线)考点15 直线与圆锥曲线相切问题 2024届高考数学考点总动员
解题方法
7 . 在平面直角坐标系
中,椭圆
的离心率为
,点
是椭圆与
轴负半轴的交点,点
是椭圆与
轴正半轴的交点,且直线
与圆
相切.
(1)求椭圆
的方程;
(2)已知斜率大于0的直线
与椭圆
有唯一的公共点
,过点
作直线
的平行线交椭圆
于点
,若
的面积为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7660b07cf2fe7e8d7ac4992969299916.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知斜率大于0的直线
![](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/5963abe8f421bd99a2aaa94831a951e9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0da03ec477a5e17b7f4de370638024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.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
8 . 已知椭圆
的离心率为
,左、右顶点分别为
,点P是椭圆上的动点,且点P与点
不重合,过其右焦点F与长轴垂直的直线与椭圆在第一象限交于点M,且
.
(1)求椭圆C的方程;
(2)设直线
的斜率分别为
,且与直线
分别交于点
,
①求:
的值;
②求证:以线段
为直径的圆过左焦点
,并求当圆的面积最小时
的值.
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953c4994cd8cccbca212900cda1b53bc.png)
(1)求椭圆C的方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
①求:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
②求证:以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09fcb20a6972108871adbf284f9e5006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e55590555905eb4f57889bbd16e39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
您最近一年使用:0次
2023-02-18更新
|
538次组卷
|
2卷引用:天津市滨海新区八所重点学校2023届高三下学期开学联考数学试题
名校
解题方法
9 . 如图,椭圆
(
)的离心率为
,其短轴和长轴的端点分别为A,B,C,D,且
.
![](https://img.xkw.com/dksih/QBM/2022/12/19/3134451182362624/3134861796286464/STEM/091444bd2e9448c28c13d8f0a112124e.png?resizew=511)
(1)求椭圆的方程;
(2)P是椭圆上位于x轴上方的动点,直线
,
与直线l:
分别交于G、H两点.若
,求点P的坐标;
(3)直线
,
分别与椭圆交于E,F两点,其中点
满足
且
.若
面积是
面积的5倍,求t的值.
![](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/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f371c0b1d573c06516ab1904d95ee49f.png)
![](https://img.xkw.com/dksih/QBM/2022/12/19/3134451182362624/3134861796286464/STEM/091444bd2e9448c28c13d8f0a112124e.png?resizew=511)
(1)求椭圆的方程;
(2)P是椭圆上位于x轴上方的动点,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e1e5a89003de4fda1dcf41565a9057.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
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2022-12-20更新
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2卷引用:天津市第四十七中学2021-2022学年高二上学期第二次月考数学试题
名校
解题方法
10 . 已知平面直角坐标系中,点
到抛物线
准线的距离等于5,椭圆
的离心率为
,且过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371e3151e76c4ab9c9a6eff1c7ad88cc.png)
![](https://img.xkw.com/dksih/QBM/2022/4/8/2953788433735680/2958471814668288/STEM/492c95c6-58c8-4402-9bd4-1928c79b8e50.png?resizew=212)
(1)求
的方程;
(2)如图,过点
作椭圆
的切线交
于
两点,在
轴上取点
,使得
,试解决以下问题:
①证明:点
与点
关于原点中心对称;
②若已知
的面积是椭圆
四个顶点所围成菱形面积的16倍,求切线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2bb2ff0cf1ae6dec186d4090d9c9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f80080fac68745fe783b879cccb6140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a2cfc8743c915f45bdccca70ab16648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371e3151e76c4ab9c9a6eff1c7ad88cc.png)
![](https://img.xkw.com/dksih/QBM/2022/4/8/2953788433735680/2958471814668288/STEM/492c95c6-58c8-4402-9bd4-1928c79b8e50.png?resizew=212)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)如图,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a085d7d76b87d6ee759f022d5384ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe2381b2935a320e50e12c573685206.png)
①证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
②若已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc727c642cbc2181476b7dd8eca471e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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6卷引用:天津市滨海新区塘沽第一中学2022届高三下学期高考模拟数学试题
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