Question

双曲线x^2/9-y^2/16=1的两个焦点为F1F2,点P在双曲线上,若PF1⊥PF2,求点P的坐标

Answer 1

由题意,两个焦点为 F1(-5,0) ; F2(5,0)

PF1⊥PF2 ,也就是说 OP = F1F2/2 =c = 5

其实 P点 就是圆 x^2+y^2=25 与 双曲线 x^2/9 - y^2/16 = 1

计算:144=16x^2-9y^2 = 16x^2-9(25-x^2)

所以 x^2=369/25 ; y^2 = 256/25

有四个交点 P(±3√41/5,±16/5 )