解题方法
1 . 如图,点A、B、C分别为椭圆
的左、右顶点和上顶点,点P是
上在第一象限内的动点,直线AP与直线BC相交于点Q,直线CP与x轴相交于点M.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/7af96dc5-c1f6-43a1-8434-369b5878f73e.png?resizew=283)
(1)求直线BC的方程;
(2)求证:
;
(3)已知直线
的方程为
,线段QM的中点为T,是否存在垂直于y轴的直线
,使得点T到
和
的距离之积为定值?若存在,求出
的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b1b8a84ae7a1b2243b78cc932860d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/7af96dc5-c1f6-43a1-8434-369b5878f73e.png?resizew=283)
(1)求直线BC的方程;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba1480cc9c2f1a5128336a7818f8189.png)
(3)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aa3adcb154f6144903d456289ecb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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