名校
解题方法
1 . 设椭圆
的左右顶点分别为
,左右焦点
.已知
,
.
(1)求椭圆方程.
(2)若斜率为1的直线
交椭圆于A,B两点,与以
为直径的圆交于C,D两点.若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44979a143cb1b38219395d4ed45ed064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cbcd330947081ded45a4cdb5e96b39.png)
(1)求椭圆方程.
(2)若斜率为1的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95485530815641d3e7b21b4e73f2b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-12-07更新
|
868次组卷
|
4卷引用:湖南省长沙市南雅中学2023-2024学年高二下学期第二次月考(5月)数学试题
湖南省长沙市南雅中学2023-2024学年高二下学期第二次月考(5月)数学试题四川省绵阳市南山中学2024届高三上学期12月月考数学(理)试题(已下线)热点7-2 椭圆及其应用(8题型+满分技巧+限时检测)(已下线)微考点6-2 圆锥曲线中的弦长面积类问题
2 . 在平面直角坐标系中,已知点
,
,点
满足
.记
的轨迹为
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2e58d7f7f5736a2ca43175ac584dae.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
您最近一年使用:0次
2023-11-09更新
|
636次组卷
|
3卷引用:湖南省长沙市部分学校2023-2024学年高二下学期入学暨寒假作业检测联考数学试卷
名校
解题方法
3 . 椭圆
上顶点为B,左焦点为F,中心为O.已知T为x轴上动点,直线BT与椭圆C交于另一点D;而P为定点,坐标为
,直线PT与y轴交于点Q.当T与F重合时,有
,且
.
(1)求椭圆C的标准方程;
(2)设T的横坐标为t,当
时,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e79685ce957fc55159d252bfa47e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41345ad137c228dc61897c489b0e8e2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4684368c49e800712bf4e2940d2ee4.png)
(1)求椭圆C的标准方程;
(2)设T的横坐标为t,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad779c4690f7697a94ff302a83ea1a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ac03e8506c3477139b3fb19573c65e.png)
您最近一年使用:0次
2023-06-15更新
|
718次组卷
|
5卷引用:湖南省长沙市雅礼中学2023-2024学年高二上学期入学考试数学试题
湖南省长沙市雅礼中学2023-2024学年高二上学期入学考试数学试题四川省成都市第七中学2024届高三零诊模拟考试数学(理)试题四川省成都市第七中学2022-2023学年高二下学期零诊数学试题(理科)(已下线)模块三 专题4 圆锥曲线中的最值和范围问题(高二人教A)(已下线)第08讲:圆锥曲线(大题) (必刷7大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
名校
解题方法
4 . 已知椭圆的焦距为
,直线
与椭圆
交于点
,若
,则椭圆
的离心率的取值范围为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-21更新
|
1314次组卷
|
4卷引用:湖南省2024届高三数学新改革提高训练二(九省联考题型)
5 . 如图所示,以原点
为圆心,分别以2和1为半径作两个同心圆,设
为大圆上任意一点,连接
交小圆于点
,设
,过点
分别作
轴,
轴的垂线,两垂线交于点
.
(1)求动点
的轨迹
的方程;
(2)点
分别是轨迹
上两点,且
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b6c260ac4010a7857457eabcb91192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/24/be09970c-aa4a-4867-aaab-836cf48ac869.png?resizew=159)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d30145021aabb04c9e730b8b356bb69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14aeac55d519010de23642ac22cfb0b.png)
您最近一年使用:0次
2023-09-23更新
|
708次组卷
|
5卷引用:湖南省岳阳市第一中学2023-2024学年高三下学期开学考试数学试题
湖南省岳阳市第一中学2023-2024学年高三下学期开学考试数学试题四川省南充市2024届高三高考适应性考试(零诊)文科数学试题四川省南充市2024届高三高考适应性考试(零诊)理科数学试题(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)福建省厦门集美中学2023-2024学年高二上学期12月月考数学试卷
名校
解题方法
6 . 已知椭圆
为其左、右焦点,
为
上点.
.当
,
面积最大.
(1)求椭圆C的离心率.
(2)过P与椭圆C相切的切线方程为
,求椭圆C的方程.
(3)在(2)的前提下,若
.过P的直线
交C的另一点
,A为C的左顶点.求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba9042bd05fb267bef023070cdcf06f.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/faa4ae8d7537feb98c7de50302705609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd15ead753cf2927f51d07c7727c6cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
(1)求椭圆C的离心率.
(2)过P与椭圆C相切的切线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60c8585792e633317e4585e177940a3.png)
(3)在(2)的前提下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f76f9480af1327b96309b1f91d137d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
2023-08-22更新
|
543次组卷
|
4卷引用:湖南省衡阳市田家炳实验中学2023-2024学年高三上学期8月测试数学试题
名校
解题方法
7 . 已知椭圆
的左、右焦点分别为
,点
是椭圆
的上顶点,
是等边三角形,
的内切圆的面积为
.
(1)求椭圆
的方程;
(2)已知
在
轴负半轴上且
,过
的直线与椭圆交于
,
两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.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/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](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/5fef472e3576506c2d4d455f70b1a090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.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/656690e5d6fe1b44a4983086229f34ae.png)
您最近一年使用:0次
2023-08-17更新
|
718次组卷
|
3卷引用:湖南省长沙市长郡中学2024届高三上学期开学考试(暑假作业检测)数学试题
解题方法
8 . 已知椭圆
的一个顶点为
,离心率为
.直线
与椭圆
交于不同的两点
,
.
(1)求椭圆
的方程;
(2)当
时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d0aafd52e26c241c46d0206f42f415.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)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
您最近一年使用:0次
9 . 已知椭圆
的离心率为
分别为椭圆
的左右顶点,
分别为椭圆
的左右焦点,
是椭圆
的上顶点,且
的外接圆半径为
.
(1)求椭圆
的方程;
(2)设与
轴不垂直的直线
交椭圆
于
两点(
在
轴的两侧),记直线
的斜率分别为
.
(i)求
的值;
(ii)若
,则求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0070ebce71a1f18e15050a2fed2fcd61.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/c5db41a1f31d6baee7c69990811edb9f.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/c352227bbb6e8c8f99c4e30185fb5869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e72b4868bdd8d15dff2211cc49cd31b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f367a71f36a7f1a5f263e47b87243f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ac9e4439b8f0c82427e410dbc86735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43d5fd4e0175a366093cb1219067d57.png)
您最近一年使用:0次
2023-08-01更新
|
678次组卷
|
3卷引用:湖南省湘潭钢铁集团有限公司第一子弟中学2024届高三8月开学考试数学试题
湖南省湘潭钢铁集团有限公司第一子弟中学2024届高三8月开学考试数学试题广东省广州大学附属中学等三校2022-2023学年高二下学期期末联考数学试题(已下线)重难点突破09 一类与斜率和、差、商、积问题的探究(四大题型)
名校
解题方法
10 . 已知椭圆
的离心率为
,右焦点为
.
(1)求此椭圆的方程;
(2)若过点F且倾斜角为
的直线与此椭圆相交于A、B两点,求|AB|的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
(1)求此椭圆的方程;
(2)若过点F且倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
您最近一年使用:0次
2023-12-10更新
|
1462次组卷
|
8卷引用:湖南省长沙市德成学校2023-2024学年高二上学期期末数学试题
湖南省长沙市德成学校2023-2024学年高二上学期期末数学试题陕西省延安市富县高级中学2021-2022学年高二上学期期末文科数学试题江西省上饶市上饶中学2024届高三上学期12月月考数学试题(已下线)模块三 专题6 大题分类练(圆锥曲线)基础夯实练 期末终极研习室(高二人教A版)(已下线)专题03 椭圆13种常见考法归类(3)新疆阿勒泰地区2023-2024学年高二上学期期末联考数学试题(已下线)专题27 直线与椭圆的位置关系及椭圆的弦长问题、面积问题(期末大题1)2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)青海省西宁市海湖中学2023-2024学年高二下学期开学考试数学试卷