椭圆X2/25+Y2/9=1上一点P到两焦点的距离之积为M则当M取最大值时点P的坐标

a=5,b=3,c=4 PF1*PF2=MPF1+PF2=2a=10 (PF1+PF2)^2=100(PF1)^2+(PF2)^2=100-2PF1*PF2=100-2M (PF1)^2+(PF2)^2≥2PF1*PF2 (PF1)^2+(PF2)^2≥2M100-2M≥2M M≤25 PF1=PF2=a=5,M取最大值=25 当M取最大值时,点P的坐标(0,±4)