名校
解题方法
1 . 已知椭圆
的左焦点为
,
是椭圆上关于原点
对称的两个动点,当点
的坐标为
时,
的周长恰为
.
(1)求椭圆的方程;
(2)过点
作直线
交椭圆于
两点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f9e88d36e731318cf9b61f9314d550.png)
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](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/6a1a9128bfafd2756206e4603126f077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b929a31d169a811004f0ecd6b7984e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86391dc521a0d9de2a6e08ed04a9ac63.png)
(1)求椭圆的方程;
(2)过点
![](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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f9e88d36e731318cf9b61f9314d550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d3b8555a8c346eacd2fe75d9d7e948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
您最近一年使用:0次
2019-05-07更新
|
1886次组卷
|
9卷引用:【市级联考】福建省宁德市2019届高三毕业班第二次(5月)质量检查考试数学理试题
【市级联考】福建省宁德市2019届高三毕业班第二次(5月)质量检查考试数学理试题2019届福建省宁德市高三质量检查数学(理)试题2020届甘肃省天水市第一中学高三下学期诊断考试数学(文)试题2020届甘肃省天水市第一中学高三下学期诊断考试数学(理)试题(已下线)专题04 圆锥曲线中的最值、范围问题(第五篇)-2020高考数学压轴题命题区间探究与突破(已下线)专题08 解析几何中的最值范围问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖(已下线)理科数学-2020年高考押题预测卷01(新课标Ⅲ卷)《2020年高考押题预测卷》江西省吉安市白鹭洲中学2020-2021学年高二12月月考数学试题江西省遂川中学2021-2022学年高二上学期第三次月考数学(理)试题(A卷)
名校
2 . 已知椭圆
,右焦点
的坐标为
,且点
在椭圆
上.
(1)求椭圆
的方程及离心率;
(2)过点
的直线交椭圆于
两点(直线不与
轴垂直),已知点
与点
关于
轴对称,证明:直线
恒过定点,并求出此定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae13b2a96f91ab64fb4948de2b0ae10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65d8dbf48fc4466396bec82e5817b00f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50ca06f64893720783b83d6f688301f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/30513ea48bc1ef3ae78adac83d894f14.png)
您最近一年使用:0次
2019-05-06更新
|
2104次组卷
|
8卷引用:江西省临川第一中学2018-2019学年高二下学期月考数学(文)试题
江西省临川第一中学2018-2019学年高二下学期月考数学(文)试题【市级联考】安徽省淮北市、宿州市2019届高三第二次教学质量检测数学(理)试题(已下线)专题06 解析几何中的定点、定值问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖(已下线)专题07 解析几何中的证明问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖江西省贵溪市第一中学2021-2022学年高二上学期第三次月考数学(理)试题陕西省西安中学2022届高三下学期二模文科数学试题江苏省南京市第一中学2022-2023学年高二上学期期末数学试题浙江省山河联盟2022-2023学年高二下学期3月联考数学试题
名校
3 . 已知椭圆
的左焦点为
,过点
的直线
交椭圆于
两点,
为坐标原点.
(1)若
的斜率为
,
为
的中点,且
的斜率为
,求椭圆
的方程;
(2)连结
并延长,交椭圆于点
,若椭圆的长半轴长
是大于
的给定常数,求
的面积的最大值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)连结
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5a9c19a17aebbc56e93d39e2b47df5.png)
您最近一年使用:0次
2019-05-05更新
|
459次组卷
|
2卷引用:【校级联考】2019年春“荆、荆、襄、宜四地七校考试联盟”高二期中联考理科数学试题
名校
解题方法
4 . 已知点
在椭圆
上,
,
是长轴的两个端点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/469eff38-2791-4409-90fd-fd39467946de.png?resizew=197)
(Ⅰ)求椭圆
的标准方程;
(Ⅱ)已知点
,过点
的直线
与椭圆的另一个交点为
,若点
总在以
为直径的圆内,求直线
的斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/c567d5e8b666bee297232fd5abd268ec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/3/469eff38-2791-4409-90fd-fd39467946de.png?resizew=197)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a62c9695f5a1691c5fe8724fa764b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](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/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2019-04-22更新
|
1794次组卷
|
5卷引用:江西省红色七校2019-2020学年高三第一次联考数学(文)试题
江西省红色七校2019-2020学年高三第一次联考数学(文)试题【市级联考】辽宁省抚顺市2019届高三第一次模拟考试数学(文)试题【市级联考】辽宁省抚顺市2019届高三第一次模拟考试数学(理)试题内蒙古集宁一中2018-2019学年高二6月月考数学(理)试题(已下线)第46讲 范围、最值、定点、定值及探索性问题(讲) — 2022年高考数学一轮复习讲练测(课标全国版)
解题方法
5 . 已知椭圆
中心在原点,焦点在
轴上,且其焦点和短轴端点都在圆
上.
(1)求椭圆
的标准方程;
(2)点
是圆
上一点,过点
作圆
的切线交椭圆
于
,
两点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e133eb3bb45bc93ecc88a186d7be937b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)点
![](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/2a30f3a8b673cc28bd90c50cf1a35281.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/aaff41080fdea43eea7efedf9ebc1498.png)
您最近一年使用:0次
2019-04-22更新
|
470次组卷
|
2卷引用:江西省南昌市三校2018-2019学年高二下学期期末数学(文)试题(一中、十中、铁一中)
名校
6 . 已知椭圆
的左右焦点分别为
,
,点
在椭圆上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb561be00616d1876fc19c608ddbc02e.png)
求椭圆的方程;
过
作与x轴不垂直的直线
与椭圆交于B,C两点,求
面积的最大值及
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0e2297e289632ffc211bd20e2e772e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a178dcca8bcd41f1bbc8a5036f900e12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb561be00616d1876fc19c608ddbc02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05fc49d7aa36586488acf96ccdd0bbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b48acde54fd48fbf883406e30972a07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2019-04-10更新
|
696次组卷
|
3卷引用:【全国百强校】江西省景德镇市景德镇一中2018-2019学年高二上学期期末考试数学(文)试题
名校
7 . 已知椭圆
为其左右焦点,
为其上下顶点,四边形
的面积为
.
(1)求椭圆
的长轴
的最小值,并确定此时椭圆
的方程;
(2)对于(1)中确定的椭圆
,设过定点
的直线
与椭圆
相交于
两点,若
,当
时,求
面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969cd893f8fe13e1487d352bd6afee88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1fd1784f10d8607df59399dbf5d105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694ed4fd4d76f641a4212908c0aa55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)对于(1)中确定的椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accf35598ee054f1bf8b6584641d6d85.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff74809c22be43d371eab398caa8ec9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65844ad7d410463e70288b6d20a5f4c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45b8b000c9c286bff8a480dbf03b513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
8 . 已知椭圆C过点
,两个焦点
.
(1)求椭圆C的标准方程;
(2)设直线l交椭圆C于A,B两点,且|AB|=6,求△AOB面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa079038f1702c4ceec7ec68dca5f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc26bb4f5b6022058c97268512c36fee.png)
(1)求椭圆C的标准方程;
(2)设直线l交椭圆C于A,B两点,且|AB|=6,求△AOB面积的最大值.
您最近一年使用:0次
2019-04-07更新
|
632次组卷
|
5卷引用:江西省赣州市五校协作体2018-2019学年高二下学期期中联考数学(理)试题
江西省赣州市五校协作体2018-2019学年高二下学期期中联考数学(理)试题【校级联考】陕西省西安地区陕师大附中、西安高级中学、高新一中、铁一中学、西工大附中等八校2019届高三3月联考数学(理)试题(已下线)2019年4月28日 《每日一题》理科 三轮复习——每周一测(已下线)2019年4月28日 《每日一题》文科 三轮复习——每周一测(已下线)黄金卷15-【赢在高考·黄金20卷】备战2021年高考数学全真模拟卷(江苏专用)
名校
9 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
经过点
,左、右焦点分别
、
,椭圆的四个顶点围成的菱形面积为
.
(Ⅰ) 求椭圆
的方程;
(Ⅱ) 设
是椭圆
上不在
轴上的一个动点,
为坐标原点,过点
作
的平行线交椭圆于
、
两点,求
的值.
![](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/36cd2eae5116601515585350e7b6ffa0.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/4e2031d209711b058f3d278ede3c1d33.png)
(Ⅰ) 求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ) 设
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](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/9f0009063fe00277645aff1be6e32471.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/c6577d89f5e9df4dbe97912c9331d375.png)
您最近一年使用:0次
2019-03-31更新
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7卷引用:江西省景德镇一中2018-2019学年高二下学期期中考试数学(文)试题
名校
10 . 在直角坐标系xOy中,已知椭圆E的中心在原点,长轴长为8,椭圆在X轴上的两个焦点与短轴的一个顶点构成等边三角形.
求椭圆的标准方程;
过椭圆内一点
的直线与椭圆E交于不同的A,B两点,交直线
于点N,若
,求证:
为定值,并求出此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cf4ac28e762fed8b0b3c8483ba37e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a302c2757cda3ee9244af4b4adad2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6e58d339c4fe57dac0c8880b029a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea987681f5636b2d51395d00bd83072.png)
您最近一年使用:0次
2019-03-24更新
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682次组卷
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3卷引用:【校级联考】江西省临川第一中学等九校2019届高三3月联考数学(文)试题