名校
解题方法
1 . 已知椭圆
,四点
中恰有三点在
上.
(1)求
的方程;
(2)若圆
的切线
与
交于点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7ff4133ed55b368b3d9edd862896ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e6bedb066ee81c299629cccf35f186.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/3825ccc273ef9a672a606432d165b866.png)
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2023-03-24更新
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773次组卷
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6卷引用:广西南宁市第三中学2022-2023学年高二下学期期中考试数学试题
名校
2 . 已知椭圆
过点
,A、B为左右顶点,且
.
(1)求椭圆C的方程;
(2)过点A作椭圆内的圆
的两条切线,交椭圆于C、D两点,若直线CD与圆O相切,求圆O的方程;
(3)过点P作(2)中圆O的两条切线,分别交椭圆于两点Q、R,求证:直线QR与圆O相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3c639884f0ea1fe96c254e452d9420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
(1)求椭圆C的方程;
(2)过点A作椭圆内的圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7121bfdb53eb8307706e8c63c4569b1d.png)
(3)过点P作(2)中圆O的两条切线,分别交椭圆于两点Q、R,求证:直线QR与圆O相切.
您最近一年使用:0次
2022-09-29更新
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859次组卷
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3卷引用:浙江省杭州市长河高级中学2021-2022学年高二下学期期中数学试题
名校
解题方法
3 . 已知椭圆
:
的离心率为
,且过椭圆的右焦点
有且仅有一条直线与圆
:
相切.
(1)求椭圆
的标准方程;
(2)设圆
与
轴的正半轴交于点
.已知直线
斜率存在且不为0,与椭圆
交于
,
两点,满足
(
为坐标原点),证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee02b034fe7987a4e67778d147e5992c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734242420d743d1cf7f597071a10575a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2021-10-02更新
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7卷引用:黑龙江省绥化市第一中学2021-2022学年高二上学期期中数学试题
黑龙江省绥化市第一中学2021-2022学年高二上学期期中数学试题沪教版(2020) 选修第一册 精准辅导 第2章 单元测试卷贵州省贵阳第一中学2022届高三上学期适应性月考卷(一)数学(文)试题贵州省贵阳第一中学2022届高三上学期适应性月考卷(一)数学(理)试题(已下线)9.6 三定问题及最值(精讲)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)一轮复习大题专练58—椭圆(定点问题)—2022届高三数学一轮复习(已下线)专题43 巧解圆锥曲线中的定点和定值问题-学会解题之高三数学万能解题模板【2022版】
解题方法
4 . 在平面直角坐标系xOy中,椭圆
的离心率为
,且过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/02f6359b-81f2-46d0-b536-1f35e9ff9aba.png?resizew=164)
(1)求椭圆E的方程;
(2)与坐标轴不垂直的直线m交椭圆E于P,Q两点,
(i)若PQ的中点R在直线
上,点
.求证:
;
(ii)若直线m与圆:
相切,求
面积的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/02f6359b-81f2-46d0-b536-1f35e9ff9aba.png?resizew=164)
(1)求椭圆E的方程;
(2)与坐标轴不垂直的直线m交椭圆E于P,Q两点,
(i)若PQ的中点R在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbd8a5d973b7a54b7605388fdcfbb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a91b14cf09b70e31b0fbe4f9f14e4b.png)
(ii)若直线m与圆:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
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名校
解题方法
5 . 已知圆O:
与直线
相切.
(1)求圆O的方程;
(2)若过点
的直线l被圆O所截得的弦长为4,求直线l的方程;
(3)若过点
作两条斜率分别为
,
的直线交圆O于B、C两点,且
,求证:直线BC恒过定点.并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4896f254406ddfe0744b63f10724e76a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8b515c0b57767af60c121f89277af2.png)
(1)求圆O的方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a06fc96b9fc095f7f77f248002749a9.png)
(3)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa64b5ac912865efd86189d4788e063.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/ddf41eff7a1310a7dcba4b236e0543ed.png)
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2020-06-11更新
|
504次组卷
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4卷引用:专题05 直线与圆综合大题18种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
(已下线)专题05 直线与圆综合大题18种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)江苏省扬州市宝应县2019-2020学年高一下学期期中数学试题(已下线)专题02 直线和圆的方程(2)江苏省泰州市口岸中学2019-2020学年高一下学期第二次月度质量检测数学试题
6 . 已知椭圆
的下焦点为
,
与短轴的两个端点构成正三角形,以
(坐标原点)为圆心,
长为半径的圆与直线
相切.
(1)求椭圆
的方程;
(2)设点
为直线
上任意一点,过点
作与直线
垂直的直线
,
交椭圆
于
两点,
的中点为
,求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/281c9349efe55d0db7395761fe9dc08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/6cad4595d5352b2884568a59d8d766a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0f7f6d4b14813f18aa16caca7dbd9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3481ecc58fb0c27daf08f7735c48d8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea52bf7f8fd9b8c250482db53bdf0705.png)
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2019-05-23更新
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2卷引用:新疆和田地区和田县2022-2023学年高二上学期11月期中教学情况调研数学试题