名校
解题方法
1 . 已知经过圆
上点
的切线方程是
.
(1)类比上述性质,直接写出经过椭圆
上一点
的切线方程;
(2)已知椭圆
,P为直线
上的动点,过P作椭圆E的两条切线,切点分别为A、B,
①求证:直线AB过定点.
②当点P到直线AB的距离为
时,求三角形PAB的外接圆方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555b3f0f1fa800a03de11718a666bdb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275bb66b8b128d42a53ab1b3dca79b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d340bd3f078b9261238d4fe59f1473c1.png)
(1)类比上述性质,直接写出经过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492b9f34846f339fd81c25dbf90282e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/275bb66b8b128d42a53ab1b3dca79b62.png)
(2)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5960f81307670e21234fff6229824af2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
①求证:直线AB过定点.
②当点P到直线AB的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448f5c45be5e4ee2e189204d334b83fd.png)
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2020-07-02更新
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647次组卷
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5卷引用:福建省福州第一中学2020届高三6月高考模拟考试数学(文)试题
福建省福州第一中学2020届高三6月高考模拟考试数学(文)试题福建省2020届高三考前冲刺适应性模拟卷(三)数学(文)试题(已下线)专题36 切线与切点弦问题(已下线)专题24 圆锥曲线八类压轴题(解答题)-3(已下线)第08讲 2.4.2圆的一般方程(10 类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)
2010·福建·三模
2 . 请阅读下列材料:对命题“若两个正实数
满足
,那么
.”
证明如下:构造函数
,因为对一切实数
,恒有
,又
,从而得
,所以
.根据上述证明方法,若
个正实数满足
时,你可以构造函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74a01d149399210cc1ce429a5b2b20e.png)
________ ,进一步能得到的结论为_________ .(不必证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://img.xkw.com/dksih/QBM/2010/5/28/1569749493014528/1569749498134528/STEM/cce5ae821deb4c158c1f3aa393088bb9.png?resizew=72)
![](https://img.xkw.com/dksih/QBM/2010/5/28/1569749493014528/1569749498134528/STEM/19ecaf9249bc4b71825a0cde7903824e.png?resizew=83)
证明如下:构造函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7ac01b73bc8f7e16d112e2359d64e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2010/5/28/1569749493014528/1569749498134528/STEM/40596f8d0360400eab85c80ca5325754.png?resizew=59)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf54b45eddef71d95462c6a71fc15ee.png)
![](https://img.xkw.com/dksih/QBM/2010/5/28/1569749493014528/1569749498134528/STEM/ba812ef51f714995b15896f3a49f5697.png?resizew=117)
![](https://img.xkw.com/dksih/QBM/2010/5/28/1569749493014528/1569749498134528/STEM/19ecaf9249bc4b71825a0cde7903824e.png?resizew=83)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2010/5/28/1569749493014528/1569749498134528/STEM/e8d930ae22424238a20e1d51a0fd808d.png?resizew=144)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74a01d149399210cc1ce429a5b2b20e.png)
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