名校
解题方法
1 . 已知椭圆
的左、右焦点分别为
,其离心率
,
和
是椭圆
上的点,且
,
的面积为
,
是坐标原点,则
的最小值为__________ .
![](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/d5c7316976a221c051a2c14df80b1347.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7affd8a277498fd39b4a2a95d649f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa50f758fb3ca54ee07f27079f8c279.png)
您最近一年使用:0次
2023-12-24更新
|
258次组卷
|
2卷引用:贵州省六盘水市水城区2023-2024学年高二上学期12月质量监测数学试题
解题方法
2 . 在平面直角坐标系中,
为坐标原点,椭圆
:
经过点
,且离心率
.
(1)求
的标准方程;
(2)经过原点的直线
与椭圆
交于
,
两点,
是
上任意点,设直线PA的斜率为
,直线PB的斜率为
,证明:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daef6a80aba5486fb5d24e44d660cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)经过原点的直线
![](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/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/2a30f3a8b673cc28bd90c50cf1a35281.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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2023-07-17更新
|
602次组卷
|
3卷引用:贵州省六盘水市2022-2023学年高二下学期期末教学质量监测数学试题
贵州省六盘水市2022-2023学年高二下学期期末教学质量监测数学试题(已下线)专题3.9 圆锥曲线中的定点、定值、定直线问题大题专项训练【九大题型】-2023-2024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)广东省汕头市潮阳一中明光学校2023-2024学年高二上学期期中测试数学试卷
解题方法
3 . 已知椭圆
的左右焦点分别为
,若椭圆
上存在点
,使得
(
为原点),
,则椭圆
的离心率
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815674e1934f2b7d281d8cf420acc5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0ae8a8ae431cdf49a0492523003a15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
您最近一年使用:0次
4 . 已知椭圆
的离心率为
、
分别为椭圆
的左、右焦点,
为椭圆
上一点,
的周长为
.
(1)求椭圆
的方程;
(2)若
,求
的面积;
(3)设
为圆
上任意一点,过
作椭圆
的两条切线,切点分别为
,判断
是否为定值?若是,求出定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbbb3c9475e24d03db0dedfc7808357f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb6f3d7540831a9e97d3b184a491.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74404619ad5699e6c44c947fb569600f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d35465f3e40ce00a1dce54b943ae183.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
您最近一年使用:0次
2022-11-29更新
|
689次组卷
|
4卷引用:选择性必修第一册综合测试卷-2022-2023学年高二上学期数学人教B版(2019)
解题方法
5 . 已知椭圆
的离心率为
,依次连接椭圆E的四个顶点构成的四边形面积为
.
(1)求椭圆E的标准方程;
(2)设椭圆E的左、右焦点分别为
,
,经过点
的直线l与椭圆E交于A,B两点,且
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆E的标准方程;
(2)设椭圆E的左、右焦点分别为
![](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/accf35598ee054f1bf8b6584641d6d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5413100518a8a6d368b9972d253d6c4b.png)
您最近一年使用:0次
2022-11-20更新
|
457次组卷
|
2卷引用:贵州省六盘水市2021-2022学年高二下学期期末质量监测数学(文)试题
名校
解题方法
6 . 已知椭圆
:
内一点
,直线
与椭圆
交于
,
两点,且
为线段
的中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b3a4a566ee5e259fec5b084635ff25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.椭圆的焦点坐标为![]() ![]() | B.椭圆![]() ![]() |
C.椭圆的离心率![]() | D.直线![]() ![]() |
您最近一年使用:0次
2021-12-25更新
|
740次组卷
|
2卷引用:选择性必修第一册综合测试卷-2022-2023学年高二上学期数学人教B版(2019)
名校
解题方法
7 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆
的方程;
(2)设直线
(不经过点
)交椭圆
于点
,
,若直线
与直线
的斜率之和为
,求证
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d8cc13666ef5e288a3c98e2fc56aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2021-08-28更新
|
1005次组卷
|
4卷引用:贵州省六盘水红桥学校2022届高三适应性月考数学(理)试题
贵州省六盘水红桥学校2022届高三适应性月考数学(理)试题云南省师范大学附属中学2022届高三高考适应性月考卷(二)数学(理)试题云南省师范大学附属中学2022届高三上学期高考适应性月考卷(二)数学(理)试题(已下线)一轮复习大题专练58—椭圆(定点问题)—2022届高三数学一轮复习
名校
解题方法
8 . 已知曲线
,给出下列四个结论:
①若
,则
是圆,其半径为
;
②若
,则
是椭圆,其离心率为
;
③若
,
,则
是两条与
轴平行的直线;
④若
,则
是双曲线,其渐近线为
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff41b0435e120094baed2e8e37353ec.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ba433823cf6f0c5d158fa909f9f600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d249094ecb996458e35182d6b461299.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66eba129d92ede31b728e2590c4db2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5beb5aaf7a9bf697e251a85bc9092f8.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bdc69abbcdf98c42b649f8d8d4cd1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9673011f3d3e5ed6ca7365e6b99afa.png)
其中所有正确结论的序号是
您最近一年使用:0次
2021-08-27更新
|
602次组卷
|
8卷引用:贵州省六盘水市红桥学校2022届高三上学期适应性月考数学(文)试题
贵州省六盘水市红桥学校2022届高三上学期适应性月考数学(文)试题贵州省六盘水红桥学校2022届高三适应性月考数学(理)试题云南省师范大学附属中学2022届高三高考适应性月考卷(二)数学(文)云南省师范大学附属中学2022届高三高考适应性月考卷(二)数学(理)试题云南省师范大学附属中学2022届高三上学期高考适应性月考卷(二)数学(文)试题云南省师范大学附属中学2022届高三上学期高考适应性月考卷(二)数学(理)试题(已下线)第02讲 双曲线-【帮课堂】2021-2022学年高二数学同步精品讲义(苏教版2019选择性必修第一册)(已下线)专题16 椭圆(选择题、填空题)-备战2022年高考数学(文)母题题源解密(全国甲卷)
解题方法
9 . 2019年12月27日20时45分,长征五号遥三运载火箭在中国文昌航天发射场点火升空,约2220秒后,将“实践二十号卫星”送入预定的运行轨道,发射任务取得圆满成功.“实践二十号卫星”的运行轨道是以地心为一个焦点的椭圆.设地球半径为
,若椭圆近地点、远地点离地面的距离大约分别是
,
,则“实践二十号卫星”运行轨道的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed3750aac23e7a8c42aab69ffe9272a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2efa1e9e71a591195af2c19f84f1252.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
10 . 已知F是双曲线
的右焦点,Q是双曲线C左支上的一点,
是y轴上的一点.当
的周长最小时,过点Q的椭圆与双曲线C共焦点,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b30352c43707c4e54b94ce5b61f2e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2750111541d454b8dd125f276e053ae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5e2bf236028751a921b5a93275729f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次