Question

双曲线X^2/a^2-y^2/b^2=1(a>0,b>0)的左、右焦点F1.F2,p是准线上一点,且pF1垂直PF2,|

Answer 1

P(a^2/c,m)

∵pF1⊥PF2,射影定理

F1^2=2c*(a^2/c+c) (1)

PF2^2=2c*(c-a^2/c) (2)

(PF1*PF2)^2=4c^2(c^2-a^4/c^2)

16a^2（c^2-a^2)=4c^4^-a^4

4a^2=c^2+a^2

3a^2=c^2

e=√3