1.问题的起源原题:已知椭圆x2/25+y2/9=1的左焦点为F1,右焦点为F2,在椭圆上是否存在点P,使∠F1PF2=90°,若存在,求出ΔF1PF2的面积;不存在,说明理由.分析:因为在椭圆上点P是短轴的端点时,∠F1PF2最大,所以只要求出此时的∠F1PF2,看它是否为不小于90°,若是钝角,则在椭圆上存在点P,使∠F1PF2=90°,且这样的点有四个;若为90°,则这样的点有两个;若小于90°,则这样 1. Origin of the Problem Original Topic: Known oval x2 / 25 + y2 / 9 = 1 The left focus is F1, the right focus is F2, there is a point P on the ellipse, so ∠ F1PF2 = 90 °, if there is Analysis: Because P is the end point of the short axis on the ellipse, ∠F1PF2 is the largest, so as long as ∠F1PF2 at this moment is obtained, it is judged whether it is not less than 90 °. If it is Obtuse, there is a point P on the ellipse so that ∠F1PF2 = 90 °, and there are four such points; if it is 90 °, then there are two such points; if less than 90 °, then