Question

若双曲线x²-y²=1上点P与两焦点连线垂直,在点P坐标

Answer 1

天线 14级 2009-07-17

焦点F(±√2,0),设P(x,y)

PF1·PF2=(x+√2)(x-√2)+y^2=x^2+y^2-2=0

x^2+y^2=2

x^2-y^2=1

x^2=1.5

y^2=0.5

P(±√6/2,±√2/2)(可任意搭配正负号,共有四个点符合要求)