解题方法
1 . 已知椭圆
,离心率为
.点
为椭圆C上一动点(其中
,
),点
,
为椭圆C左右焦点,直线
与直线
在一象限交于点
,则线段
长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a304696b261e993dcaa4038627ac9bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13747fa9a42164caebe2c9b7c5d06d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b170470d02c85c1be9a3faff5eca0de.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/56f7299e8c8873f61b5ce5d3f2333b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
A.2 | B.![]() | C.1 | D.4 |
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2 . 下列说法正确的有( )
A.函数![]() ![]() |
B.满足:![]() ![]() |
C.若![]() ![]() |
D.命题“![]() ![]() |
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解题方法
3 . 已知抛物线C:
,
,过点Р的直线
交抛物线C于A,B两点,线段AB中点为
,直线
经过点D且垂直于y轴,直线
经过点
且垂直于直线
,记
,
相交于点N,下列说法正确的序号为____ .
①
;②
的斜率为
;③
;④点N在定直线
上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842747ef9bfbd8893e3d7a2272a70e62.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa4e9d7d044658001c41e2ca2dfb82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41e4234c48e25329a4f52d1f2f26e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
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2卷引用:四川省绵阳市2022-2023学年高二上学期期末数学理科试题
4 . 已知圆O:
,直线
.
(1)若圆O的弦AB恰好被点
平分,求弦AB所在直线的方程;
(2)点Q是直线l上的动点,过Q作圆O的两条切线,切点分别为C,D,求直线CD经过的定点;
(3)过点
作两条相异的直线,分别与圆O相交于E,F两点,当直线ME与直线MF的斜率互为倒数时,求线段EF的中点G的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd89a03660c85fb78bd7fe82ee3068c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41888144f7eb9ca029d624560530d82.png)
(1)若圆O的弦AB恰好被点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
(2)点Q是直线l上的动点,过Q作圆O的两条切线,切点分别为C,D,求直线CD经过的定点;
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cda12642d59a5817e8990c43de20535.png)
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解题方法
5 . “木桶效应”是一个有名的心理效应,是指木桶盛水量的多少,取决于构成木桶的最短木板的长度,而不取决于构成木桶的长木板的长度,常被用来寓意一个短处对于一个团队或者一个人的影响程度.某同学认为,如果将该木桶斜放,发挥长板的作用,在短板存在的情况下,也能盛较多的水.根据该同学的说法,若有一个如图①所示圆柱形木桶,其中一块木板有缺口,缺口最低处与桶口的距离为
,若按图②的方式盛水,木桶倾斜到与水平面成
时,水面刚好与左边缺口最低处
和右侧桶口
齐平,并形成一个椭圆水面,且
为椭圆的长轴,则该椭圆的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/cd6f2a5c-98d9-4e7a-98d4-2b69527fc316.png?resizew=259)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe8dc472dade6cea6943164792ab532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa29fe6cd9eb51c184f6299d437375cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/cd6f2a5c-98d9-4e7a-98d4-2b69527fc316.png?resizew=259)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:四川省资阳市2022-2023学年高二下学期入学检测(上学期期末质量监测)理科数学试题
四川省资阳市2022-2023学年高二下学期入学检测(上学期期末质量监测)理科数学试题四川省资阳市2022-2023学年高二上学期期末理科数学试题(已下线)专题20 椭圆-1(已下线)模块一 专题4《圆锥曲线》单元检测篇 B 提升卷 期末终极研习室(高二人教A版)
名校
6 . 下列命题是真命题的是( )
A.“若x,y互为相反数,则![]() |
B.“偶函数的图象关于y轴对称”是特称命题 |
C.“![]() ![]() ![]() |
D.若![]() |
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7 . 已知动点
在直线
上,以点
和
为焦点的椭圆经过点
,当椭圆的长轴长最小时,点
的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4ce9d2ca51d84ac4f6a0e8ec7adcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a18a7caa080988802ba1145b4fe4203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知抛物线
及圆C:
.
(1)过圆心C作直线
与抛物线和圆交于四个点,自上而下依次为A,M,N,B,若
成等差数列,求直线
的方程;
(2)过抛物线上一动点P(P的横坐标大于
)作圆C的两条切线分别交y轴于E,F两点,求线段EF的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd6047b670ad125d505010dd4576067.png)
(1)过圆心C作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16661b4917f86b0ebe754c55a9f9a8f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)过抛物线上一动点P(P的横坐标大于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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名校
解题方法
9 . 已知直线
与椭圆
:
交于
两点,弦
平行
轴,交
轴于
,
的延长线交椭圆于
,下列说法正确的个数是( )
①椭圆
的离心率为
;
②
;
③
;
④以
为直径的圆过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/8a726e4d-1875-444a-b3ce-9dc9ca9dd4fd.png?resizew=206)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8481f8c148f7ee6e0ee000d38ea62ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
①椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5020a41ba83aa373e56279a8da9fb82f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e68736e6fe6530d1b4bd4e8e9885de2a.png)
④以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/8a726e4d-1875-444a-b3ce-9dc9ca9dd4fd.png?resizew=206)
A.1个 | B.2个 | C.3个 | D.4个 |
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3卷引用:四川省德阳市德阳市第五中学2022-2023学年高二上学期期中数学(理)试题
2022高三·全国·专题练习
10 . 如图,中心在原点
的椭圆
的右焦点为
,长轴长为
.椭圆
上有两点
、
,连接
、
,记它们的斜率为
、
,且满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/baa6db7f-47c5-470a-b427-305483b59662.png?resizew=229)
(1)求椭圆
的标准方程;
(2)求证:
为一定值,并求出这个定值;
(3)设直线
与椭圆
的另一个交点为
,直线
和
分别与直线
交于点
、
,若
和
的面积相等,求点
的横坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967dc76338e277e690e0e524d4179e1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023037c7a3e31ba698c39f9b52db2515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157a01e29b471bbcae32d0e129a5b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93f1438d9a45a9561fba2183ee1c1a2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/baa6db7f-47c5-470a-b427-305483b59662.png?resizew=229)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f6c5fd93aed88bec58002a20ea2e90.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42af8cdea9c5269c17aebb086afdd136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b05c3b58de848e6a33cb450fd39776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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4卷引用:四川省巴中市恩阳区2022-2023学年高二上学期期末数学试题
四川省巴中市恩阳区2022-2023学年高二上学期期末数学试题(已下线)专题12平面解析几何必考题型分类训练-4广东省广州市四校联考2022-2023学年高二上学期期中数学试题上海市曹杨第二中学2023届高三模拟数学试题