名校
解题方法
1 . 已知椭圆
的离心率为
,且椭圆上的点到焦点的最长距离为
.
(1)求椭圆
的方程:
(2)直线
(不过原点
)与抛物线
相交于
两点,以
为直径的圆经过原点
,且此直线
也与椭圆
相交于
两点,求
面积的最大值及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a04c700a775406b4b2f5a27c88f871.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ed6bee57f4526320197d6a7474386f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-12-22更新
|
681次组卷
|
4卷引用:四川省绵阳南山中学实验学校2023-2024学年高二上学期12月月考数学试题
解题方法
2 . 已知函数
定义域为R,且满足
,
,
,给出以下四个命题:
①
;
②
;
③
;
④函数
的图象关于直线
对称.
其中正确命题的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf116ecbdb894c1d05d5b3b5203c10a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0082b730e39498e7bc4ae201c0282128.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2efb7a2b238982ec6ca55287ca3f721c.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e298fe246eef819dd9b1edabe3bb9cb.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbafc0688ba92842df9b7fb507b0bf01.png)
④函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a2e637d559bfae29c1d30c2b50d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
其中正确命题的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
3 . 设
、
分别是椭圆
的左、右焦点,若_____,
请在以下两个条件中任选一个补充在横线上并作答.
①四点
、
、
、
中,恰有三点在椭圆
上;
②椭圆
经过点
,
与
轴垂直,且
.
(注:如果选择多个条件分别解答,则按第一个解答计分).
(1)求椭圆
的离心率;
(2)设
是椭圆
的上顶点,过
任作两条互相垂直的直线分别交椭圆
于
、
两点,过点
作线段
的垂线,垂足为
,判断在
轴上是否存在定点
,使得
的长度为定值?并证明你的结论.
![](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)
请在以下两个条件中任选一个补充在横线上并作答.
①四点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f05b989842734d1afd9429d15f5484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ccebafcbec8ab901145708edf2b3da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbdd68297be3e412c68d27457a9f8224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9085f45a27c7122adddfec645b233e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e97a3b321e8f5a5cc526b2b8daa702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183b6a0cef4256c9696a5bca31053da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3c9cedff7811b2f9e565bdf42bfee1.png)
(注:如果选择多个条件分别解答,则按第一个解答计分).
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a81443594dd303ef713b62378dd5c20.png)
您最近一年使用:0次
名校
解题方法
4 . 已知点
,
,曲线
上的任意点
满足
,曲线
与双曲线
的两条渐近线相交于四个点,按顺时针排列依次为
,且
,则
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee80939187a84e1863eeb192a301c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed154dc722c0576255346d7f237969ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7798d9c992c27e91b6297a635a004637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bbfb6436cdda3be72735316cb54cd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a6b8043a86f590437b76f5ceb3308c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2023-12-22更新
|
221次组卷
|
2卷引用:四川省绵阳市南山中学2023-2024学年高二上学期12月月考数学试题
解题方法
5 . 已知正方形
边长为
,
是正方形
的外接圆的一条动弦,
,
为正方形
边上的动点,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040d6732d32d552cb60f1a9430b67c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07116f9f184757ad645ab1308af2f182.png)
您最近一年使用:0次
6 . 已知函数
,
,其中实数
.
(1)求
在
上的单调区间和极值;
(2)若方程
有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e349f49908801a73999320f7a49820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c773633c5cfdccc24ee6388dc11b88e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abf906e9c6ecf603de9b41098a1c0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaeaa6bb42e960bc4c86303277caf49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
7 . 已知函数
与其导函数为
定义域均为
,且
满足
,
,
,给出以下四个命题:
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e298fe246eef819dd9b1edabe3bb9cb.png)
③函数
的图象关于直线
对称 ④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0d337b876fee3527d1f58d062f6505.png)
其中正确命题的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf116ecbdb894c1d05d5b3b5203c10a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0082b730e39498e7bc4ae201c0282128.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae17aeafc0a40b66bf6f65db99c237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e298fe246eef819dd9b1edabe3bb9cb.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a2e637d559bfae29c1d30c2b50d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0d337b876fee3527d1f58d062f6505.png)
其中正确命题的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
名校
解题方法
8 . 如图,已知四棱锥
的底面
是直角梯形,
,
,
,
平面
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af260e0d98c95d1e092dc4c6d348e3ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.平面![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-12-21更新
|
415次组卷
|
4卷引用:四川省遂宁市蓬溪中学校2023-2024学年高二上学期12月月考数学试题
名校
9 . 定义在
上的函数
满足
,且当
时,
,
,对
,使得
,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/322eb46d949b9580bcc057d146b7fc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad814089e37543b2f547af9ae75b6dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3983fbea281cf9678113d4c469e9b171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76ba1c1cef5f0e6efdca5e436122412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1099eb8da78386f101ef7db3ad94e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347ac85769012f89d1f9951684e1d7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
10 . 已知
分别为椭圆
的左、右焦点,A为右顶点,B为上顶点,若在线段AB上有且仅有一个点P使
,则椭圆
离心率的取值范围为______ (写成集合或区间形式).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70ac71550d9280fe969ded947e7e2b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1086f33fd5082e6d19694093c4174c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2023-12-20更新
|
1054次组卷
|
5卷引用:四川省成都市蓉城名校2023-2024学年高二上学期期末联考数学试题