1 . 在平面直角坐标系中,已知
为坐标原点,点
为直线
:
与椭圆
:
的一个交点,且
,
.
(1)证明:直线
与椭圆
相切;
(2)已知直线
与椭圆
:
交于
,
两点,且点
为
的中点.
(i)证明:椭圆
的离心率为定值;
(ii)记
的面积为
,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152236216f8d1cb39b261108e8fc8b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a980c55b1f6cee5807fcea8bf613df33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b1c78d909cf94234a6c2a8fe28c057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db60cf63a8024ff5b47b1e47090a817c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9d71d4a47bd6f425c2260fc142361c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/91edc7e2d4811f5ea6c01284cf00393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(i)证明:椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48057a284f5314eabea64989e32819aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159013e30c1e03bbc0c0d2a0df0dd3a1.png)
您最近一年使用:0次
2021-05-08更新
|
1324次组卷
|
5卷引用:湖南省长沙市雅礼中学等十六校2022届高三下学期第一次联考数学试题
10-11高三下·湖南长沙·阶段练习
名校
解题方法
2 . 给定椭圆
,称圆心在原点
,半径为
的圆是椭圆
的“海中圆”.若椭圆
的一个焦点为
,其短轴上的一个端点到
的距离为
.
(1)求椭圆
的方程和其“海中圆”方程;
(2)点
是椭圆
的“海中圆”上的一个动点,过点
作直线
,
,使得
,
与椭圆
都只有一个交点.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215bb197d894dc7d3c96228778d04684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3224fbb9ff94c62064d9e86ba021ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/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/1ce08b357f11ef44c3e8207ac574422a.png)
您最近一年使用:0次
2020-09-23更新
|
295次组卷
|
5卷引用:2011届湖南省长沙市长望浏宁四县高三3月调研考试数学理卷
(已下线)2011届湖南省长沙市长望浏宁四县高三3月调研考试数学理卷2019届广西柳州市高三10月模拟考试数学(理)试题广西贵港市高级中学2022届高三毕业班5月模拟考试数学(理)试题贵州省遵义市2018-2019学年度高二上学期期末文科数学试题福建省泰宁第一中学2018-2019学年高二上学期第二阶段考试数学(理)试题
名校
解题方法
3 . 已知点
为椭圆
上任意一点,直线
与圆
交于
,
两点,点
为椭圆
的左焦点.
(1)求证:直线
与椭圆
相切;
(2)判断
是否为定值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/482aa1008b1009aa649b2e44a5d05a16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0eea02b3e07ba8b9771e9401a81f983.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36719f1e764ee0e719b65c49fae84677.png)
您最近一年使用:0次
2020-04-22更新
|
459次组卷
|
3卷引用:湖南师大附中2020届高三下学期月考(七)理科数学试题
名校
4 . 已知椭圆
的右焦点为
,原点为
,椭圆
的动弦
过焦点
且不垂直于坐标轴,弦
的中点为
,过
且垂直于线段
的直线交射线
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/c5b4215c-2b32-4f04-aafd-73f7bf2ac30a.png?resizew=324)
(Ⅰ)证明:点
在定直线上;
(Ⅱ)当
最大时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e9f7d1272b7344346b58b660aa260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/c5b4215c-2b32-4f04-aafd-73f7bf2ac30a.png?resizew=324)
(Ⅰ)证明:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a59b1be6398640d8db0680f4bdd71189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
您最近一年使用:0次
名校
5 . 设D是圆O:x2+y2=16上的任意一点,m是过点D且与x轴垂直的直线,E是直线m与x轴的交点,点Q在直线m上,且满足2|EQ|
|ED|.当点D在圆O上运动时,记点Q的轨迹为曲线C.
(1)求曲线C的方程.
(2)已知点P(2,3),过F(2,0)的直线l交曲线C于A,B两点,交直线x=8于点M.判定直线PA,PM,PB的斜率是否依次构成等差数列?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e589def3e7fe21b601bc6d5144073202.png)
(1)求曲线C的方程.
(2)已知点P(2,3),过F(2,0)的直线l交曲线C于A,B两点,交直线x=8于点M.判定直线PA,PM,PB的斜率是否依次构成等差数列?并说明理由.
您最近一年使用:0次
2019-05-07更新
|
907次组卷
|
10卷引用:【市级联考】湖南省长沙市2019届高三下学期第二次模拟考试数学(理)试题
【市级联考】湖南省长沙市2019届高三下学期第二次模拟考试数学(理)试题【市级联考】湖南省长沙市2019届高三下学期第二次模拟考试数学(文)试题【市级联考】广西南宁市2019届高三毕业班第一次适应性测试数学(理科)试题【市级联考】广西南宁市2019届高三毕业班第一次适应性测试数学(文)试题【市级联考】湖南省湘潭市2019届高三下学期第二次模拟考试数学(文)试题【市级联考】湖南省湘潭市2019届高三下学期第二次模拟考试数学(理)试题【市级联考】辽宁省辽阳市2019届高三下学期一模数学(理科)试题2020年普通高等学校招生全国统一考试理科数学样卷(五)2020年普通高等学校招生全国统一考试 文科数学样卷(五)重庆市第十一中学2020届高三下学期6月月考数学(理)试题