1 . 已知椭圆
的焦距为2,两个焦点与短轴一个顶点构成等边三角形.
(1)求椭圆
的标准方程;
(2)设
,过点
的两条直线
和
分别交椭圆
于点
和点
(
和
.不重合),直线
和
的斜率分别为
和
.若
,判断
是否为定值,若是,求出该值;若否,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9195fe550aabe5aefb626892f4483ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/70c6fa2ef2d5a1be4c7c2bd3be4b4366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2024-06-11更新
|
787次组卷
|
4卷引用:海南省部分学校2024届高三下学期高考考前押题(二)数学试题
名校
2 . 如图所示,已知圆
,点
,点
为圆
上的动点,线段
的垂直平分线
和半径
相交于点
.
![](https://img.xkw.com/dksih/QBM/2022/3/27/2945501013377024/2946788584751104/STEM/8c523281-2d8e-4fd5-a06c-e6977aad610b.png?resizew=171)
(1)当点
在圆上运动时,求点
的运动轨迹
的方程;
(2)判断直线
和曲线
的位置关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdc28de4b46c7a176ba6858a856a918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/2022/3/27/2945501013377024/2946788584751104/STEM/8c523281-2d8e-4fd5-a06c-e6977aad610b.png?resizew=171)
(1)当点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
名校
3 . 已知直线
与椭圆
交于
两点,
与直线
交于点
(1)证明:
与C相切;
(2)设线段
的中点为
,且
,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daaa79c480ddd9840991398ff67a5505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55ede98a46253c74ab6790e396d4038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701fd8d82e2ce8985f41fb0cf8524ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
(2)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/875d94138025df50536b04e8b0caa5cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
2019-04-15更新
|
970次组卷
|
16卷引用:【市级联考】海南省海口市2019届高三高考调研测试数学(文科)试题
【市级联考】海南省海口市2019届高三高考调研测试数学(文科)试题【市级联考】河南省新乡市2019届高三第三次模拟测试数学文科试题【全国百强校】宁夏石嘴山市第三中学2019届高三下学期三模考试数学(文)试题陕西省宝鸡市2021届高三下学期大联考文科数学试题【市级联考】河北省邯郸市2018-2019学年高二下学期期中考试数学(理科)试题【市级联考】河北省邯郸市2018-2019学年高二下学期期中考试数学(文)试题2019届贵州省黔南州高三上学期期末数学试卷理科试题2019届贵州省黔南州高三上学期期末数学试卷文科试题甘肃省天水市第一中学2020-2021学年高三上学期第五次考试数学(文)试题(已下线)甘肃省天水市第一中学2020-2021学年高三第五次考试(下学期开学考试)数学(文)试题山西省大同市灵丘一中、广灵一中2020-2021学年高二下学期期中联考数学(文)试题山西省大同市灵丘一中、广灵一中2020-2021学年高二下学期期中联考数学(理)试题安徽省六安市第一中学2022届高三上学期第二次月考文科数学试题广西壮族自治区贺州市昭平中学2021-2022学年高二下学期第一次月考数学(理)试题青海省西宁市大通回族土族自治县2021-2022届高三数学(文)开学摸底考试试题甘肃省天水市秦州区第一中学2020-2021学年高三下学期数学(文)开学考试试题
名校
4 . 如图,点
在椭圆
上,且点
到两焦点的距离之和为6.
(2)设与
(
为坐标原点)垂直的直线交椭圆于
(
不重合),求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94718313450e8a66d1fd47728891375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4cfef623a9534b5708df5f95f1760a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658aa70a197c830aa765f2f7ea4c86c5.png)
您最近一年使用:0次
2017-09-02更新
|
1485次组卷
|
5卷引用:海南省(海南中学、文昌中学、海口市第一中学、农垦中学)等八校2018届高三上学期新起点联盟考试数学(理)试题
5 . 设椭圆
,定义椭圆
的“相关圆”方程为
.若抛物线
的焦点与椭圆
的一个焦点重合,且椭圆
短轴 一个端点和其两个焦点构成直角三角形.
(Ⅰ)求椭圆
的方程和“相关圆”
的方程;
(Ⅱ)过“相关圆”
上任意一点
的直线
与椭圆
交于
两点.
为坐标原点,若
,证明原点
到直线
的距离是定值,并求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/56afc5a624634baf9baec213d168d965.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/253e88c11236431280145d6cd6f000e0.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/5cbb63c62d644ec59ac7538f9d249f48.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/5fb669fe466d43fc9ee205915cfd633f.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/253e88c11236431280145d6cd6f000e0.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/253e88c11236431280145d6cd6f000e0.png)
(Ⅰ)求椭圆
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/253e88c11236431280145d6cd6f000e0.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/82e21fdb8cbd4260812a54b696ca9905.png)
(Ⅱ)过“相关圆”
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/82e21fdb8cbd4260812a54b696ca9905.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/4db8d7e2e1a64e3a8ef3d2a042910840.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/04d81cc80e484800a627346c0162ad65.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/253e88c11236431280145d6cd6f000e0.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/3da383c4cc1f4c889e47c4827692f911.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/5f44075e9e7c4610a775eee1b87d3643.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/497082593a4d49dd88246073e271c763.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/5f44075e9e7c4610a775eee1b87d3643.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/1aaa2cfc28e0428192ecec5dfd149b88.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572927734513664/1572927740076032/STEM/c774ef38bea9455ca68a9093db57a162.png)
您最近一年使用:0次