在一次习题课中,我们做了一道解析几何习题,同学们大胆类比探索,热情很高,得出了一些结论,现展示如下:2原题已知椭圆C:x2/4+y2=1的左右顶4点分别是A1、A2,直线l:x=2(2)~(1/2)与x轴交于点D,点P是椭圆上的异于A1、A2的动点,直线A1P、A2P分别交l于E、F两点,求证:|DE|·|DF|恒为定值.证明设E(2(2)~(1/2),e), In an exercise class, we did an analytical geometry exercises, the students bold analogy to explore, a high degree of enthusiasm, come to some conclusions, are shown below: 2 original question known oval C: x2 / 4 + y2 = 1 Left and right top 4 points are A1, A2, the line l: x = 2 (2) ~ (1/2) and the x-axis intersect at the point D, the point P is elliptical point of departure from A1, A2, , A2P, respectively, to pay l, E, F points, verify: | DE | · | DF | constant for the fixed value. Prove that E (2