名校
1 . 如图,在
中,已知
,其内切圆与AC边相切于点D,且
,延长BA到E,使
,连接CE,设以E,C为焦点且经过点A的椭圆的离心率为
,以E,C为焦点且经过点A的双曲线的离心率为
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df1ac3ab8d3ce5e61fd2f89761f80976.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/120f812ad42739155a1337e7d5a7bcf7.png)
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2024-04-10更新
|
1591次组卷
|
5卷引用:湖北省黄冈市浠水县第一中学2024届高三下学期第三次高考模拟数学试题
湖北省黄冈市浠水县第一中学2024届高三下学期第三次高考模拟数学试题山东省实验中学2024届高三下学期第一次模拟考试数学试题(已下线)第10题 共焦点的椭圆离心率问题(压轴小题)(已下线)压轴题02圆锥曲线压轴题17题型汇总-1(已下线)平面解析几何-综合测试卷B卷
名校
解题方法
2 . 已知椭圆C:
的左、右焦点分别为
,
,P为C上一点,满足
,以C的短轴为直径作圆O,截直线
的弦长为
,则C的离心率为( )
![](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/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ec189df9aa2b3c46de719d0057a05f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-14更新
|
1062次组卷
|
5卷引用:湖北省襄阳市第四中学2024届高三下学期高考最后一次数学测试题
解题方法
3 . 已知椭圆
的离心率为
,
,
,
,
,设P为椭圆C上一点
的面积的最大值为
.
(1)求椭圆C的方程;
(2)当P在第三象限,直线
与y轴交于点M,直线
与x轴交于点N,求证:四边形
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87e24ea042ecf3f25150338e22b45b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374cdec65a41dc616f6f099551880d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆C的方程;
(2)当P在第三象限,直线
![](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/e53abbd672b82a02c4975f99fbbd2c37.png)
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解题方法
4 . 已知椭圆
的左焦点为
,过原点
的直线
交椭圆于
,
两点,点
在第二象限,且
(如图),则椭圆的离心率为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc653312ef32b1e98025b79963cc47d.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d8030884be606b9710f058cf49dd81a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/6af3fb0f-65ef-45ee-a96d-26e0441d4326.png?resizew=150)
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名校
解题方法
5 . 如图,已知椭圆
的离心率为
,点
在
上.
(1)求
的方程;
(2)设点
关于原点
对称点为
为
上异于
的动点,直线
分别交
轴于
两点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253bfd4a02407a65c97c811f7c8118a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/20/07e39702-9a98-4458-9295-330715b5326a.png?resizew=162)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdd498c29baff72302805b1044285db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5671fb25040a712a49e8c8148d67d300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb40dae2b0f4048d3fabff25e6cbe443.png)
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2024-02-23更新
|
297次组卷
|
2卷引用:湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)
名校
解题方法
6 . 已知椭圆
的离心率为
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113a2cb11fb93bd71c7f13dde9b24812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
A.![]() ![]() | B.![]() | C.![]() ![]() | D.1 |
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2024-02-20更新
|
832次组卷
|
2卷引用:湖北省武汉外国语学校2023-2024学年高二上学期期末考试数学试题
名校
解题方法
7 . 已知椭圆
的离心率为
,左、右焦点分别为
,
,点P为椭圆C上任意一点,
面积最大值为
.
(1)求椭圆C的方程;
(2)过x轴上一点
的直线与椭圆交于A,B两点,过A,B分别作直线
的垂线,垂足为M,N两点,证明:直线
,
交于一定点,并求出该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆C的方程;
(2)过x轴上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724e11601d3807c120713018d3405d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
解题方法
8 . 已知
是椭圆
上一点.
(1)求
的离心率;
(2)过点
作两条互相垂直且斜率均存在的直线
与
交于
两点,
与
交于
两点,
分别为弦
和
的中点,直线
与
轴交于点
,试判断
是否为定值.若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20f651031c6025b6f33498e9698576db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817e9ed9062ace5344891c1cde6e1c03.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e646897fd3cd0581d197306d43cb1601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f752c13a92273c899ba39bfb5665ed00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/80cb9f37d7a4f30c37dc24baf89c93bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ab7024f73ff0cb7e6a48197538a91e.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆C:
(
,
)右焦点为F,M,N是椭圆上关于原点对称的两点,且不在坐标轴上,线段FM、FN的中点分别为A,B,且
,则椭圆C的离心率可以为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc1eb76fe74cba30f7cbcde349ba80da.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 已知椭圆
的离心率为
,左,右焦点分别为
,
,过
且倾斜角为
的直线与椭圆C交于A,B两点(点A在第一象限),P是椭圆C上任意一点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
A.a,b满足![]() | B.![]() ![]() |
C.存在点P,使得![]() | D.![]() |
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