1 . 已知
、
分别是椭圆
的左、右焦点,且焦距为
,动弦
平行于
轴,且
.直线
,设直线
与椭圆
交于
、
两点.
(1)求椭圆
的方程;
(2)若
,求实数
的取值范围;
(3)若直线
、
、
的斜率成等比数列(其中
为坐标原点),求△
的面积的取值范围.
![](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/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e20934258090465f9ec853458a98833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f44c9010af5e7b8c487b125dd053d35.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8b709da2c8d8e649eede7bc963953e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
您最近一年使用:0次
2 . 已知椭圆
的左、右顶点分别为A,B,O为坐标原点,点P在C上(异于A,B两点),直线
,
的斜率之积为
,点
在C上.
(1)求C的方程;
(2)过椭圆C的右焦点F的直线
与C交于D,E两点,过线段
的中点G作直线
的垂线,垂足为N,记
的面积为S,直线
,
的斜率分别为
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/d78fd95f89dec2d373fa57f02acd739f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67baac84cf5c95d06d50c36cab7c68.png)
(1)求C的方程;
(2)过椭圆C的右焦点F的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e00bf73d03dded1cf5f83cc5339361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.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/ca640540d5152619c1d7eac53a2bdfbd.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
是圆
上不同的两点,椭圆
的右顶点和上顶点分别为
,直线
分别是圆
的两条切线,
为椭圆
的离心率.下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1325c6fe42a9e5c04520d8a9bb6821b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4372c60e72bc1f82072a2c31cd51a7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddfa25e097562b856ddd5e7c0758ee2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.若椭圆![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2023-07-20更新
|
1525次组卷
|
7卷引用:山西省运城市运城中学2023届高三第二次模拟数学试题
山西省运城市运城中学2023届高三第二次模拟数学试题河北省张家口市2023届高三三模数学试题江西省萍乡市安源中学2022-2023学年高二下学期期末考试数学试题(已下线)3.1.2 椭圆的简单的几何性质(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)专题11 平面解析几何-2(已下线)专题18 椭圆、双曲线、抛物线小题河北省廊坊市香河县第一中学2023-2024学年高三下学期模拟考试数学试卷
解题方法
4 . 已知椭圆
的焦距为
,左、右顶点分别为
,上顶点为B,且
.
(1)求椭圆C的方程;
(2)若过
且斜率为k的直线l与椭圆C在第一象限相交于点Q,与直线
相交于点P,与y轴相交于点M,且
.求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1735708848cfde06947647a29687a76.png)
(1)求椭圆C的方程;
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f69a7effc74ab83bd02bb4c2d9e9716.png)
您最近一年使用:0次
2023-04-23更新
|
306次组卷
|
3卷引用:山西省运城市2024届高三上学期期末调研测试数学试题
名校
解题方法
5 . 已知椭圆
上有点
,左、右焦点分别为
.
(1)求椭圆的标准方程;
(2)若点Q为椭圆的上顶点,椭圆上有异于Q的两点
满足
,求证:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc2210a7e09298897f6585ad08a70d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.png)
(1)求椭圆的标准方程;
(2)若点Q为椭圆的上顶点,椭圆上有异于Q的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0615bfe416db14d15783f764613ae84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2022-12-06更新
|
778次组卷
|
8卷引用:山西大学附属中学校2022-2023学年高二上学期12月月考数学试题
名校
解题方法
6 . 已知椭圆
:
的左、右焦点分别为
,
,点
是椭圆
的一个顶点,
是等腰直角三角形.
(1)求椭圆
的标准方程;
(2)过点
分别作直线
,
交椭圆于A,
两点,设两直线
,
的斜率分别为
,
,且
,证明:直线
过定点.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ed90ebf0061c8a79beed307fc1719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f9a699aededce0ad803bf8257fbbcb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.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/c2b1bd378406bcd8156a56469f9300f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-08-12更新
|
2612次组卷
|
10卷引用:山西省山西大附属中学2023届高三上学期8月模块诊断数学试题
山西省山西大附属中学2023届高三上学期8月模块诊断数学试题2023版 北师大版(2019) 选修第一册 突围者 第二章 专项拓展训练3 与圆锥曲线有关的定值、定点、定直线问题湖北省襄阳市第五中学2022-2023学年高三上学期暑期返校数学试题辽宁省辽西联合校2022-2023学年高二上学期期中考试数学试题(已下线)专题32 一类与斜率和、差、商、积问题的探究-1(已下线)全册综合测试卷-提高篇-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)第25讲 圆锥曲线直线圆过定点问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)甘肃省兰州市教育局第四片区2022-2023学年高二下学期联片办学期中考试数学试题广东湛江市2022-2023学年高二下学期期末数学试题广东省珠海市实验中学2024届高三上学期8月适应性考试数学试题
解题方法
7 . 已知圆
:
,动圆
过点
且与圆
相切,记动圆圆心
的轨迹为曲线C.
(1)求曲线C的方程;
(2)过点
的直线m交椭圆C于点M、N,且满足
(E为圆E的圆心),求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8911f31214a92bcf5a2918a83ccdf9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求曲线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ff5934f25c3eb2653400af26ef9f97.png)
您最近一年使用:0次
2022-01-24更新
|
625次组卷
|
3卷引用:山西省朔州市怀仁市2023届高三二模数学试题
名校
解题方法
8 . 已知
,
分别为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/470cde3e5244dfbbb08078d8e5717ccb.png)
的左、右焦点,椭圆上任意一点
到焦点距离的最小值与最大值之比为
,过
且垂直于长轴的椭圆
的弦长为
.
(1)求椭圆
的标准方程;
(2)过
的直线与椭圆
相交的交点
、
与右焦点
所围成的三角形的内切圆面积是否存在最大值?若存在,试求出最大值;若不存在,说明理由.
![](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/470cde3e5244dfbbb08078d8e5717ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04239f37cf5218093585663ccb5688eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/a3fb78c5f885034612c0e030b920143d.png)
您最近一年使用:0次
2021-09-12更新
|
1575次组卷
|
14卷引用:山西省稷山中学2021-2022学年高二上学期第二次月考数学试题
山西省稷山中学2021-2022学年高二上学期第二次月考数学试题河南省顶级名校2021-2022学年高三上学期9月开学联考数学(理)试题湘豫名校联考2022届高三上学期8月数学文科试题河南省顶级名校2021-2022学年高三上学期9月开学联考数学(文)试题四川省成都市树德中学2021-2022学年高三上学期10月阶段性测试数学(文)试题四川省成都市树德中学2021-2022学年高三上学期10月阶段性测试数学(理)试题吉林省白城市第一中学2021-2022学年高二上学期期中数学试题(已下线)一轮复习大题专练56—椭圆(面积最值问题1)—2022届高三数学一轮复习福建省福州屏东中学2021-2022学年高二上学期期中考试数学试题(已下线)3.1.1椭圆及其标准方程(备作业)-【上好课】2021-2022学年高二数学同步备课系列(人教A版2019选择性必修第一册)河北省廊坊市第一中学2021-2022学年高一上学期12月考试数学试题(已下线)专题31 圆锥曲线存在性问题的五种类型大题100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)江苏省南通市如东高级中学2022-2023学年高三上学期12月阶段测试数学试题河北省2023届高三模拟数学试题
名校
解题方法
9 . 如图,已知
,
分别是椭圆
:
的左、右焦点,过
的直线
与过
的直线
交于点
,线段
的中点为
,线段
的垂直平分线
与
的交点
(第一象限)在椭圆上,若
为坐标原点,则
的取值范围为( )
![](https://img.xkw.com/dksih/QBM/2020/7/7/2500980319559680/2501550599520256/STEM/9c8b12b1f0ea4fdcb86c7d116ac8e262.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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A.![]() | B.![]() | C.![]() | D.![]() |
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2020-07-08更新
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14卷引用:2020届山西省运城市高中联合体高三模拟(二)数学(文)试题
2020届山西省运城市高中联合体高三模拟(二)数学(文)试题安徽省名校学术联盟2020届高三下学期押题卷文科数学试题北师大版(2019) 选修第一册 必杀技 第二章 素养检测贵州省铜仁市思南中学2021届高三第十次月考数学(文)试题贵州省铜仁市思南中学2021届高三第十次月考数学(理)试题苏教版(2019) 选修第一册 必杀技 第三章 素养检测黑龙江省鸡西市密山市第一中学2021-2022学年高二上学期期中数学试题(已下线)专题6.3 期中押题检测卷(考试范围:第1-3章)3(难)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册) (已下线)专题10 圆锥曲线与方程-备战2022年高考数学学霸纠错(全国通用)(已下线)3.1 椭圆的几何性质-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) (已下线)专题44 巧求圆锥曲线中的最值和范围问题-学会解题之高三数学万能解题模板【2022版】(已下线)考点8-2 椭圆及其性质(文理)江西省新余市第一中学2022-2023学年高二(零班)上学期开学考试数学试题江苏省连云港市灌南高级中学2021-2022学年高二普通班上学期10月月考数学试题
名校
解题方法
10 . 设椭圆
的左顶点为
,右顶点为
,已知椭圆
的离心率为
,且以线段
为直径的圆被直线
所截的弦长为
.
(1)求椭圆的方程;
(2)记椭圆
的右焦点为
,过点
且斜率为
的直线交椭圆于
两点.若线段
的垂直平分线与
轴交于点
,求
的取值范围.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698d7ad4f0b131f8287883ed42f79fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
(1)求椭圆的方程;
(2)记椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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3卷引用:2020届山西省晋中市高三普通高等学校招生统一模拟考试(四模)数学(文)试题