解题方法
1 . 在直角坐标系
上取两个定点
,再取两个动点
,且
.
(1)求直线
与
交点的轨迹M的方程;
(2)已知点
是轨迹M上的定点,E,F是轨迹M上的两个动点,如果直线AE的斜率
与直线AF的斜率
满足
,试探究直线EF的斜率是否是定值?若是定值,求出这个定值,若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728b3360d5c6394457b907f1cbc31a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a461fda226f0bd4110de4dec466ab5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb4d5fd550c84d02dd68e0b39b1b7c0.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a112d71e48de9093b85d248c6ee2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d9474ef6e91a668a30481a7c9ca34f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f32ef32dfc25c0432e5be48d2e7c372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff20ed0b3544f29756b858798054a3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54b9320227bac7e03eb44d06bf824ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb1bcd06e9f4b4f8589391a55dad676f.png)
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