名校
解题方法
1 . 已知A,B分别为椭圆
左、右顶点,F是椭圆E的右焦点,其离心率
,点
在椭圆E上,其中
.记直线
的斜率分为
,且
.
(1)求E的标准方程和实数
的值;
(2)若动点
(异于顶点)是椭圆E上的动点,过点P的直线l的方程为:
,且直线
交直线l于点
,直线
交直线l于点
,试探究
是否为定值?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d3f39015d0d4ef7a057422bbe41e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166925a9c1ee0f691316608193ed049e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cada79783bb8229895fa4d635a284d.png)
(1)求E的标准方程和实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbc9b4166327ee2ca655cb68372d4c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853e3c15d116fb61f236ab239c50b114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683cf78b53b5e8f8a6580ebcefd1facb.png)
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