解题方法
1 . 定义:若椭圆
上的两个点
,
满足
,则称A,B为该椭圆的一个“共轭点对”,记作
.已知椭圆C:
上一点
.
(1)求“共轭点对”
中点B所在直线l的方程.
(2)设O为坐标原点,点P,Q在椭圆C上,且
,(1)中的直线l与椭圆C交于两点
.
①求点
,
的坐标;
②设四点
,P,
,Q在椭圆C上逆时针排列,证明:四边形
的面积小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3170fac2bc69eb892f933884eab77a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e82db0c7d2c362cf4a70027aaa19be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ab5ed3dd54f42da747b01afdb7b031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50edfb9ed0d50d6f35ad6a130208d307.png)
(1)求“共轭点对”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e82db0c7d2c362cf4a70027aaa19be.png)
(2)设O为坐标原点,点P,Q在椭圆C上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9ab90788bfa77a7287d14ce54efb02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6bfbdd01cbd00209f89e5d703f0caa.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
②设四点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3227c1743747bfe46953dc2280792d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
您最近一年使用:0次
2 . 焦点为
的抛物线
与圆
交于
两点,其中
点横坐标为
,方程
的曲线记为
,
是曲线
上一动点.
在抛物线上且满足
,求直线
的斜率;
(2)
是
轴上一定点. 若动点
在
上满足
的范围内运动时,
恒成立,求
的取值范围;
(3)
是曲线
上另一动点,且满足
,若
的面积为4 ,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd64825e3ff912ad3cae60e6b6dca488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c97938d07092ac2803ff89a47e5b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcec04cff66ddf1c021d73d6c681ebb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360d86f0ec1c4d9d0dfc06a9064db0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388f9a492789afe93cd09bced064e06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff8450b7dd0330a9686594a14baa9f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0b68e4289ee07e6a7d1dbea801aecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a52c17a41524894bb6932b11181e6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e29303195c563855aee4c14cbcb9bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2021-05-05更新
|
709次组卷
|
7卷引用:上海市嘉定区第二中学2022届高三下学期开学考试数学试题
上海市嘉定区第二中学2022届高三下学期开学考试数学试题上海市杨浦区2021届高三二模数学试题(已下线)押第20题 解析几何-备战2021年高考数学(文)临考题号押题(全国卷1)(已下线)押第20题 解析几何-备战2021年高考数学(理)临考题号押题(全国卷1)江西省宜春市丰城市第九中学2022-2023学年高二重点班(28、29班)上学期期末考试数学试题(已下线)压轴题圆锥曲线新定义题(九省联考第19题模式)练(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 16-19
名校
解题方法
3 . 给定椭圆
(
),称圆心在坐标原点
,半径为
的圆是椭圆
的“伴随圆”,若椭圆
右焦点坐标为
,且过点
.
(1)求椭圆
的“伴随圆”方程;
(2)在椭圆
的“伴随圆”上取一点
,过该点作椭圆的两条切线
、
,证明:两切线垂直;
(3)在双曲线
上找一点
作椭圆
的两条切线,分别交于切点
、
,使得
,求满足条件的所有点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.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/b707fdf035eb2fb4467958893c60381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a904c923ca5efc55a8a158e74ae4b0b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0210da9839dce53ae6f0533764d24ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(3)在双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/3842d532ecdfd77186b3999d1357149d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
4 . 我们称点P到图形C上任意一点距离的最小值为点P到图形C的距离,记作
.
(1)求点
到抛物线
的距离
;
(2)设
是长为2的线段,求点集
所表示图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a421e5d3b3752b9e1f04c30799bace.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d2cbdff8483ebba708857163ef1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72a421e5d3b3752b9e1f04c30799bace.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1981136b22c60c0d63bae0e334fa53.png)
您最近一年使用:0次
名校
解题方法
5 . 给定椭圆
,称圆心在原点
、半径为
的圆是椭圆
的“卫星圆”,若椭圆
的离心率为
,点
在
上.
(1)求椭圆
的方程和其“卫星圆”方程;
(2)点
是椭圆
的“卫星圆”上的一个动点,过点
作直线
、
使得
,与椭圆
都只有一个交点,且
、
分别交其“卫星圆”于点
、
,证明:弦长
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f21c7162941d2b54ebafb1795599195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2020-08-05更新
|
1118次组卷
|
15卷引用:广东省东莞市石竹实验学校2022-2023学年高二下学期开学学情调查数学试题
广东省东莞市石竹实验学校2022-2023学年高二下学期开学学情调查数学试题2020届山东省青岛市高三上学期期末数学试题2020届山东省潍坊市奎文区第一中学高三下学期3月月考数学试题2020届山东省菏泽一中高三下学期在线数学试题2020届山东省菏泽一中高三2月份自测数学试题(已下线)冲刺卷01-决战2020年高考数学冲刺卷(山东专版)(已下线)提升套餐练01-【新题型】2020年新高考数学多选题与热点解答题组合练山东省济钢高中2019-2020学年高三3月质量检测试题(已下线)第8篇——平面解析几何-新高考山东专题汇编(已下线)强化卷01(4月)-冲刺2020高考数学之拿高分题目强化卷(山东专版)(已下线)大题专练训练28:圆锥曲线(切线问题)-2021届高三数学二轮复习重庆市缙云教育联盟2022届高三上学期9月月度质量检测数学试题(已下线)专题16 圆锥曲线常考题型04——定值问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)山东省青岛市实验高中(青岛第十五中学)2020-2021学年高二上学期期中考试数学试题山东省潍坊市昌乐第一中学2024届高三上学期模拟预测数学试题