名校
解题方法
1 . 已知
是椭圆
的两个焦点,过
的斜率存在且不为0的直线
与椭圆
交于
,
两点,
是
的中点,
为坐标原点,则下列说法正确的序号是______ .
①椭圆
的离心率为
;
②存在点
使得
;
③若
,则
;
④
与
的斜率满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cce619f899a16eacda7a59c064bc967.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/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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288060bacca802a86ff209ddfd412e18.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0348cfd22b4dfc68468aa7abd42684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ed9d97b8745ed1c15349ea3fffc299.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7226f75fe372bf8d5aaa94101444bd6f.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
是椭圆与双曲线的公共焦点,
是它们的一个公共点,且
,线段
的垂直平分线过
,若椭圆的离心率为
,双曲线的离心率为
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727c32b3f38d2e1f464711e1547c1b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec10dc93eec473a71420bb4639e97c.png)
您最近一年使用:0次
2023-01-20更新
|
605次组卷
|
5卷引用:河北省秦皇岛市昌黎文汇学校2020-2021学年高二上学期期末数学试题
解题方法
3 . 已知
为椭圆
的左、右焦点,
为
的中点(
为坐标原点),过
的直线
交
于第一象限内
点,
到直线
的距离为
,且
轴,则椭圆
的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d107e77106ff1a9cb76b504bbc99bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2298721a6c96c6a0529917677d8dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0803835d6f594a60bd16c823e3ad2cd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
名校
4 . 已知椭圆
的离心率
,则m的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39ad8dccf74c05b92e5b7dd8f582789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d4dabdef38ec7f8f6d61a3f43e8b09.png)
A.3 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-03-23更新
|
295次组卷
|
3卷引用:河北省博野中学2021-2022学年高二上学期期中数学试题
河北省博野中学2021-2022学年高二上学期期中数学试题第2章 圆锥曲线测试题 -2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册(已下线)3.1.2 椭圆的简单几何性质【第二课】“上好三节课,做好三套题“高中数学素养晋级之路
名校
解题方法
5 . 已知椭圆
:
的左、右焦点分别为
,
,离心率为
,且
过点
.
(1)求椭圆
的标准方程;
(2)若过点
的直线
与椭圆
相交于
,
两点,求
的最大值;
![](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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b3560b239bca664c50848502cc878b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](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/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/0eedc3420cb964301090179a29b1a958.png)
您最近一年使用:0次
2021-12-29更新
|
1191次组卷
|
2卷引用:河北省部分学校2021-2022学年高二上学期第三次月考数学试题
名校
解题方法
6 . 已知点
在椭圆
上,
与
关于原点对称,
,
交
轴于点
,
为坐标原点,
,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/b96214ad04975700936f48ddb36c74f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b73d42b77599fe0249e2d60b4211f7c8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-12-28更新
|
2228次组卷
|
7卷引用:河北省金科大联考2022届高三上学期12月质量检测数学试题
河北省金科大联考2022届高三上学期12月质量检测数学试题山东省枣庄市2021-2022学年高二上学期期末数学试题(已下线)解密14 椭圆方程(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(新高考专用)辽宁省大连市金普新区省示范性高中联合体2021-2022学年高三第四阶段考试(下学期开学考试)数学试题吉林省长春市希望高中2021-2022学年高二上学期期末数学试题重庆市二0三中学校2022-2023学年高二上学期期末数学试题(已下线)模块一 专题13 圆锥曲线的方程1
名校
解题方法
7 . 给出如下四个命题不正确的是( )
A.方程![]() | B.椭圆![]() ![]() |
C.抛物线![]() ![]() | D.双曲线![]() ![]() |
您最近一年使用:0次
2021-12-24更新
|
915次组卷
|
12卷引用:河北省博野中学2021-2022学年高二上学期12月月考数学试题
河北省博野中学2021-2022学年高二上学期12月月考数学试题福建省尤溪第一中学2021~2022学年高二上学期第二次月考数学试题广东省信宜市第二中学2021-2022学年高二下学期月考一数学试题福建省福州华侨中学2021-2022学年高二下学期期末考试数学试题新疆维吾尔自治区喀什第二中学2022-2023学年高二上学期期中考试数学试题江苏省连云港市2022-2023学年高二上学期期末调研数学试题(8)广西桂林市逸仙中学2022-2023学年高二上学期11月期中数学试题重庆市荣昌永荣中学校2021-2022学年高二上学期期末数学试题云南省宣威市第三中学2022-2023学年高二下学期第三次月考数学试题江西省宜春市宜丰县宜丰中学2022-2023学年高二上学期期末数学试题云南省昆明市昆明师专附中2021-2022学年高二上学期期末数学试题湖北省鄂州市第二中学2023-2024学年高二上学期12月月考数学试题
名校
解题方法
8 . 已知椭圆
的中心在原点,焦点在
轴上,长轴长为4,离心率等于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
的方程
(2)设
,若椭圆E上存在两个不同点P、Q满足
,证明:直线PQ过定点,并求该定点的坐标.
![](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/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcadfe766e5ce650c693bb394fb7473d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d484860d9392ecacc942edecd37b6dd.png)
您最近一年使用:0次
2021-12-24更新
|
1284次组卷
|
4卷引用:河北省廊坊市第一中学2021-2022学年高二上学期11月考试数学试题
名校
解题方法
9 . 已知P是椭圆
:
上的动点,过
直线与椭圆交于
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fef53df361100dd33c7ac4a561d6c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee1c96a487881b995de89287a84dc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
A.![]() ![]() | B.当![]() ![]() ![]() ![]() |
C.![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2021-12-22更新
|
1388次组卷
|
3卷引用:河北徐水综合高级中学2021-2022学年高二上学期第二次月考数学试题
解题方法
10 . 已知点
,
和直线
.
(1)若
是直线
上一个动点,求
的最小值;
(2)若椭圆
以
为焦点且与直线
有公共点,求椭圆
的离心率的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc13f1877a59f1cedcc8eb9c5ea23a2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d46e3ac39fe24c845b379cdf5df402.png)
(2)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次