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【简答题】
如图,椭圆E: =1(a>b>0)的左焦点为F 1 ,右焦点为F 2 ,离心率e= .过F 1 的直线交椭圆于A、B两点,且△ABF 2 的8. (1)求椭圆E的方程; (2)设动直线l:y=kx+m与椭圆E有且只有一个公共点P,且与直线x=4相交于点Q.试探究:在坐标平面内是否存在定点M,使得以PQ为直径的圆恒过点M?若存在,求出点M的坐标;若不存在,说明理由.
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