解题方法
1 . 已知
,函数
.
(1)若
,求
在点
处的切线方程;
(2)求证:
;
(3)若
为
的极值点,点
在圆
上.求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe45993e6bd636a4f34886bb3d72f42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788ebf70de03fb27efdb04252024b55a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd277b65fe7f9896b600a7950e57e47.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca84dff2367d3127e8ea7775981345b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763f6c02b45500e5a42ce71f5e10ed96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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真题
2 . 设
,在平面直角坐标系中,已知向量
,向量
,
,动点
的轨迹为E.
(1)求轨迹E的方程,并说明该方程所表示曲线的形状;
(2)已知
,证明:存在圆心在原点的圆,使得该圆的任意一条切线与轨迹E恒有两个交点A,B,且
(O为坐标原点),并求出该圆的方程;
(3)已知
,设直线
与圆C:
(1<R<2)相切于A1,且
与轨迹E只有一个公共点B1,当R为何值时,|A1B1|取得最大值?并求最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d1dbacb32c6aa64b346cfc40c5e7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069d5e4878e17bf1f2bd494d5f1c8447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc74c79951a73d068aa2229f7d415d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a32a090bc3ff8e2e53407c2ae4084cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
(1)求轨迹E的方程,并说明该方程所表示曲线的形状;
(2)已知
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/ad66f3538bea4def8499012dccd571f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada5c15d7b42b2fb2836c3478ae5fb34.png)
(3)已知
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/ad66f3538bea4def8499012dccd571f5.png)
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/eb968bca05eb47dcb4e86eb45f24c831.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d443779a9f5889e921a60e5b452a926f.png)
![](https://img.xkw.com/dksih/QBM/2010/3/12/1569631062581248/1569631152578560/STEM/eb968bca05eb47dcb4e86eb45f24c831.png)
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2019-01-30更新
|
2832次组卷
|
4卷引用:2009年普通高等学校招生全国统一考试文科数学(山东卷)
2009年普通高等学校招生全国统一考试文科数学(山东卷)(已下线)2012-2013学年四川省外语实验学校高二4月数学试卷高中数学解题兵法 第三十四讲 分类讨论是一种重要的解题策略(已下线)专题23 圆锥曲线中的最值、范围问题 微点1 圆锥曲线中的最值问题
名校
解题方法
3 . 已知圆
过点
,
,且圆心
在直线
上,过点
的直线交圆
于
两点,过点
分别作圆
的切线,记为
.
(1)求圆
的方程;
(2)求证:直线
的交点都在同一条直线上,并求出这条直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ed90ebf0061c8a79beed307fc1719a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895b45ce9162e12904639417fa1bfbd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7053364523e655abed4a0c887fae69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d347ce38af382b8667283eef0e38b167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
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