8.P点在椭圆x^2/45+y^2/20 =1上,F1,F2是椭圆的焦点,若PF1⊥PF2,则P点的坐标是

问题描述:

8.P点在椭圆x^2/45+y^2/20 =1上,F1,F2是椭圆的焦点,若PF1⊥PF2,则P点的坐标是
答案为(3,4)(3,-4)(-3,4)(-3,-4)

a=3√5,b=2√5,c=5,F1,F2的坐标为(5,0)、(-5,0),P点的坐标是(x,y)PF1+PF2=2a=6√5PF1^2+PF2^2=2a=(2c)^2=100PF1=4√5或PF1=2√5,即PF1=a-ex=3√5-√5x/3=4√5或PF1=a-ex=3√5-√5x/3=2√5x=3或x=-3所以P点的坐...