题目
题型:不详难度:来源:
设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105928-56002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105928-79984.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105928-13138.png)
(2)如果
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105929-94015.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105929-15611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105929-57528.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105929-66279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105930-18104.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105930-41814.png)
∴△>0
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105930-25482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105931-35356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105931-43513.png)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105931-32971.png)
∴重心G的轨迹方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105931-86722.png)
………6分(范围不对扣1分)
②
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105932-59955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105932-48689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105932-12450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105932-32511.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105933-32412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105933-57339.png)
那么AB的中垂线方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105933-63084.png)
令△ABF外接圆圆心为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105934-41854.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105934-25212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105934-29352.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105935-94120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105935-63622.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105935-51659.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105935-28070.png)
∴所求的圆的方程为
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105936-61491.png)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105917-76285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105918-50982.png)
已知抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105854-25138.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105855-50511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105855-52459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105855-88601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105855-44899.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105855-32590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105856-26488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105855-32590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105856-16946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105856-31025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105856-57702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105857-41527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105857-49543.png)
(1)求抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105856-16946.png)
(2)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105857-87268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105857-82074.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105856-16946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105858-46216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105858-91186.png)
证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105858-97821.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105843-58361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191025/20191025105843-46860.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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