已知A(-2,0),B(2,0),点C、D依次满足 | AC |=2, AD = 1 2 ( AB + AC ) . (1)求点D的轨迹; (2)过点A作直线l交以A、B为焦点的椭圆于M、N两点,线段MN的中点到y轴的距离为 4 5 ,且直线l与点D的轨迹相切,求该椭圆的方程; (3)在(2)的条件下,设点Q的坐标为(1,0),是否存在椭圆上的点P及以Q为圆心的一个圆,使得该圆与直线PA,PB都相切,如存在,求出P点坐标及圆的方程,如不存在,请说明理由.
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