对于问题:“已知曲线
与曲线
有且只有两个公共点,求经过这两个公共点的直线方程”.某人的正解如下:曲线
的方程与曲线
的方程相加得
,这就是所求的直线方程.理由是:①两个方程相加后得到的表示直线;②两个公共点的坐标都分别满足曲线
的方程与曲线
的方程,则它们就满足两个方程相加后得到的方程;③两点确定一条直线.用类似的方法解下列问题:若曲线
与曲线
有且只有3个公共点,且它们不共线,则经过3个公共点的圆方程为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34fa8c1bad3319f37abb8b7ef321835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326241d820ba58a9c54dd477e9f6e014.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41905d6209592e179bdcc32ce210df3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3620b5ca85d6c3ce9987f36d04b4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a62369d5323226084e19b26dfa4636.png)
更新时间:2020-02-28 23:18:10
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解题方法
【推荐1】过三点
、
、
的圆的半径为______ ,圆心坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1bf8899b8865afe102aec97e340e45.png)
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【推荐2】已知点
在圆
上,点P关于直线
的对称点也在圆C上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
____ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915651fc9cdae8de0bf6fddbaad641d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89358edaf8bf5154415bf42b6dd96f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1cb41222d27da278a922db1cd5cb34.png)
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【推荐1】求“方程
的解”有如下解题思路:设
,则
在
上单调递减,且
,所以原方程有唯一解
.类比上述解题思路,方程
的解为________ .
![](https://img.xkw.com/dksih/QBM/2014/5/21/1571732118372352/1571732124082176/STEM/7860ce1fa5e04ddc92780212d823efb3.png?resizew=96)
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【推荐2】“求方程
的解”可假设
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.类比上述解法,则方程
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef18670761b20b08d0db1a5f0307e05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d8732cf2de6bda2d5a7e244ba05b6a.png)
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