1 . 已知椭圆
的离心率为
,其左、右顶点分别为
,左右焦点为
,点
为椭圆上异于
的动点,且
的面积最大值为
.
(1)求椭圆
的方程及
的值;(
、
分别指直线
的斜率)
(2)设动直线
交椭圆
于
两点,记直线
的斜率为
,直线
的斜率为
,且
.
①求证:直线
过定点;
②设
的面积分别为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc157c66eef6affd86e48432176c4240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9626bd07f966ea26a51dcd8ceba04ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edf32f4d595c02a8c0f7cc5f8fd0c931.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d4a832771ba45d407f31000c8fcf37.png)
(2)设动直线
![](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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2659bf25c135efc1e342b5f5e92d48d2.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9a706cc0a6ad655c22d40cea0efa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c4295f918205f5598ecc9a96d8867.png)
您最近一年使用:0次
解题方法
2 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)若点
是
图象上一点,点
是
图象上一点,在当
时,求
,
两点之间的最近距离;
(2)若函数
在
上单调递减,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702f71fb0a6c22cf5ec4b3fbe387c5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8d507d3032a43acef8cb62ccc8944e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
3 . 已知圆C经过点
和点
,且圆心在直线
上,则圆C的标准方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56339a78e814bc0cb8f45cb2e23515bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6868a51ea0a78f2605d3d1cbe701351b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
您最近一年使用:0次
2023-04-21更新
|
774次组卷
|
6卷引用:内蒙古包头市2023届高三二模文科数学试题
内蒙古包头市2023届高三二模文科数学试题内蒙古包头市2023届高三二模理科数学试题内蒙古自治区乌兰察布市2023届高三二模理科数学试题(已下线)专题14解析几何(选填)海南省陵水黎族自治县陵水中学2024届高三上学期第六次模拟测试数学试题(已下线)第02讲 2.4圆的方程+2.5直线与圆,圆与圆的位置关系(1)
4 . 已知复数
与
在复平面内对应的点关于直线
对称,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef015c99536d13f1386bbb9a1dcaecea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d4d30c0f79dcb11ab161c49fa57ee0.png)
A.![]() | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
5 . 已知直线
与直线
互相垂直,垂足为
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f752458b5870d09a72b7d9d19dec3b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2667eb9615bff56621f26b3734966e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758c7726a4ed76236206eba5f5b5bcb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ede0c7822059ae81dec24383d75886.png)
A.6 | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
6 . 如图,已知正方体
的棱长为2,P为底面正方形ABCD内(含边界)的一动点,则下列结论正确的序号有______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/e6aef2bf-758e-41dc-a1b9-e2cefe8f58a4.png?resizew=169)
①存在点P,使得
平面
;
②三棱锥
的体积为定值;
③当点P在棱CD上时,
的最小值为
;
④若点P到直线
与到直线AD的距离相等,CD的中点为E,则点P到直线AE的最短距离是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/25/e6aef2bf-758e-41dc-a1b9-e2cefe8f58a4.png?resizew=169)
①存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f86e2d69b11402d9d6cbb06e057778a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0a582c36d62d83c16425b2f54b4354.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e7361ffb6d22b31453f636ef5bf45a.png)
③当点P在棱CD上时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f75c2df8aa495f5aff68c20130caee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2b42b76abb6aca31dabaaf2456825d.png)
④若点P到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748ce363bf0d656545db3cc6c8d01690.png)
您最近一年使用:0次
2023-03-23更新
|
849次组卷
|
4卷引用:内蒙古赤峰市林东第一中学2023届高三5月数学模拟考试题
7 . 已知直线
与圆
交于A,B两点,则弦
的长为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8464bb7caf9d2badd4bd2dc3b4f9cebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2023-03-16更新
|
458次组卷
|
2卷引用:内蒙古包头市2023届高三下学期一模文科数学试题
解题方法
8 . 已知椭圆
的长轴长为4,离心率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/5152203e-cf01-4b30-9a58-6d8b9cfa33d7.png?resizew=229)
(1)求椭圆C的方程;
(2)已知点
,
,直线l过坐标原点O交椭圆C于P,Q两点(点A,B位于直线l的两侧).设直线AP,AQ,BP,BQ的斜率分别为
,
,
,
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/5152203e-cf01-4b30-9a58-6d8b9cfa33d7.png?resizew=229)
(1)求椭圆C的方程;
(2)已知点
![](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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3307e11f7e6896e32aa510bbed949ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d338fc48134a0b2ae59b1c290a51a96a.png)
您最近一年使用:0次
解题方法
9 . 双曲线
的左顶点为A,点M,N均在C上,且关于y轴对称.若直线
,
的斜率之积为
,则C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021·浙江·模拟预测
解题方法
10 . 若
、
满足线性约束条件
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78471ab85d6fc04c1b73a900105bb3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe3addf56c9e572aa4570c2c46486a.png)
A.有最小值![]() | B.有最小值![]() |
C.有最大值![]() | D.有最大值![]() |
您最近一年使用:0次
2021-05-21更新
|
838次组卷
|
5卷引用:内蒙古赤峰市八校2023届高三第三次统一模拟考试联考文科数学试题
内蒙古赤峰市八校2023届高三第三次统一模拟考试联考文科数学试题(已下线)2021年浙江省高考最后一卷数学(第五模拟)四川省遂宁市2021-2022学年高三上学期零诊模拟试题(二)数学(文科)试题(已下线)第09节 简单的线性规划问题(已下线)考点28 直线与方程-备战2022年高考数学(理)一轮复习考点微专题