名校
1 . 已知椭圆
的离心率为
,
是
上一点,
,
,是
的两个焦点,且
.
求椭圆
的方程;
设直线
交椭圆
于
两点,
为坐标原点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35cc9f5236efef08ca67543434c39ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c38805c09dcfbcc42103308975a74.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/a09a8ac969e5cec3be6abf4ff44c692e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6758b8b074d33ea9e82818593656e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac452d435c3a344897bd8a69dc2b44ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9aec2e1020524a21bec15c62feb224d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ed6bee57f4526320197d6a7474386f.png)
您最近一年使用:0次
2019-03-18更新
|
634次组卷
|
3卷引用:【市级联考】湖南省湘潭市2018-2019学年高二第一学期期末考试数学(文)试题
2 . 椭圆C的中心为坐标原点O,焦点在x轴上,B为上顶点,F为右焦点,若点O到直线BF的距离为焦距的
.
求椭圆C的离心率;
已知直线l不垂直于坐标轴且直线l过点F与椭圆C交于M,N两点,
与
共线.
求直线l的斜率;
设P为椭圆C上任意一点,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb84f6fbac102ccf326b2223d69cb7cc.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/0b134e16e6b4d24345b92014d1975b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef244910dcaee5202f4b08dc612bf7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c512c047783c07da1d4f4455a4033ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/876959b9f90f2379cf3d0927a8e31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4164b9bee4b6306528ac09a83cef4b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb75be30114a0934ab8d647c4c63a34.png)
您最近一年使用:0次
名校
解题方法
3 . 已知点
,过点
作抛物线
的切线
,切点
在第二象限.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/29bfbb27-f644-4c57-a20c-ae8d75809509.png?resizew=225)
求切点
的纵坐标;
有一离心率为
的椭圆
恰好经过切点
,设切线
与椭圆的另一交点为点
,记切线
的斜率分别为
,
,
,若
,求椭圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e8766616ce41fdee67f0ba4059d7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10b3710fd4e512ff3d61bb6a6ed8d14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/29bfbb27-f644-4c57-a20c-ae8d75809509.png?resizew=225)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9c6fe12d3a9727e00ef87a630302ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fc64ac5f9a1deacec3865970183a74.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1501f835e2524494d06e1f54d6041fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f980ccb6f902d460d0ea2920bfe2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b2046b273243141c4a84dc675a67bd9.png)
您最近一年使用:0次
2019-03-13更新
|
872次组卷
|
4卷引用:西藏自治区拉萨市拉萨中学2019-2020学年高二第六次月考数学理科试卷
名校
4 . 已知椭圆方程为
,双曲线方程为
,若该双曲线的两条渐近线与椭圆的四个交点以及椭圆的两个焦点恰为一个正六边形的六个顶点,则椭圆的离心率与双曲线的离心率之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d125266f7bffeb5292742d81fd65432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14dc42421bd7343ce22d3158bddf86a.png)
您最近一年使用:0次
2019-03-04更新
|
878次组卷
|
6卷引用:【市级联考】江苏省淮安市2018-2019学年高二第一学期期末调研测试数学试题
名校
5 . 已知
分别是椭圆
的上下两个焦点,若椭圆上存在四个不同点
,使得
的面积为
,则椭圆
的离心率的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94956cd2837f297f76d8964ae44ff1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-03-02更新
|
2492次组卷
|
7卷引用:福建省厦门二中2020-2021学年高二(10月份)月考数学试题
名校
6 . 已知椭圆
的两个焦点分别为
,离心率为
,过
的直线
与椭圆
交于
两点,且
的周长为8.
(1)求椭圆
的方程;
(2)直线
过点
,且与椭圆
交于
两点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968bc863acdb4f2b0cba33157363e711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b799737e84f54908b8700fbaf1f96a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cfa1e7ffae662aefb49a44c52d4954d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94165c5047e68e952df7a8dc6dc32fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e41ee0f9a5bd498c3b42e062cc2ca4.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe355d4e2b592beaeb135030f7677396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b09e2d46f94b9ca3caf3f8283619c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46a208a6fb8e750c993f1ae959f4506.png)
您最近一年使用:0次
2019-02-28更新
|
1089次组卷
|
7卷引用:【全国百强校】陕西省西安市西安中学2018-2019学年高二上学期期末考试理科数学试题
7 . 已知椭圆
的长轴长为
,离心率为
.
![](https://img.xkw.com/dksih/QBM/2019/2/15/2141245377748992/2141374092107776/STEM/98880955e0f64b3ea1629254cc4a7854.png?resizew=238)
(1)求椭圆
的方程;
(2)过动点
的直线交
轴于点
,交椭圆
于点
,
(
在第一象限),且
是线段
的中点.过点
作
轴的垂线交椭圆
于另一点
,延长
交椭圆
于点
.
①设直线
、
的斜率分别为
,证明
为定值;
②求直线
斜率取最小值时,直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://img.xkw.com/dksih/QBM/2019/2/15/2141245377748992/2141374092107776/STEM/98880955e0f64b3ea1629254cc4a7854.png?resizew=238)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d8a5982a53874dd3e97d9af6d7942ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/dad2a36927223bd70f426ba06aea4b45.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/6c8ffe24cf9f327aeb241225ab15ab1a.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a2cc28a0fc418c4edbd702190dd77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21451f7a858408ce47fee33c798ba9d5.png)
②求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
您最近一年使用:0次
解题方法
8 . 已知椭圆的中心在原点,
为椭圆的一个焦点,离心率
,过
作两条互相垂直的直线
,
,
与椭圆交于
两点,
与椭圆交于
两点,且
四点在椭圆上逆时针分布.
(1)求椭圆的标准方程;
(2)求四边形
面积的最大值与最小值的比值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d054e17d28ec3c190340f2055e93102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
(1)求椭圆的标准方程;
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2019-02-11更新
|
505次组卷
|
2卷引用:【市级联考】辽宁省葫芦岛市2018-2019学年高二上学期期末考试 数学(理)试题
9 . 已知离心率为
的椭圆
的左、右焦点分别为
、
,点
在椭圆
上,点
为
的内心,且
、
、
的面积分别为
、
、
,若
,则
的值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/dad2a36927223bd70f426ba06aea4b45.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/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0837f5fccc63b02cc191cb3d1c576185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb086d78c571ce5646e609122b674620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ff410a277986fc6045c1cb36f89e34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb74fd6a84af622da60993838516477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c634c249015ccf476788450980f2b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3325f6afd0b358aade1a624aadf2c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567dd5f9272ab7228ef9de5e01b4c174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b1003f3b5e76b58f785d4e27f40ff2.png)
您最近一年使用:0次
2019-02-10更新
|
1890次组卷
|
4卷引用:【市级联考】四川省绵阳市2018-2019学年高二上学期期末教学质量测试数学(文)试题
名校
10 . 已知椭圆:
的左右焦点分别为
,
为椭圆上的一点
与椭圆交于
.若
的内切圆与线段
在其中点处相切,与
切于
,则椭圆的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a498efa7b1c44bafa4327a512e9c55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-02-01更新
|
2213次组卷
|
5卷引用:【全国百强校】山西省长治二中2018-2019学年高二上学期期末考试数学(理)试题