答:
双曲线(x^2)/a^2 -(y^2)/b^2=1
因为:|PF1|=4|PF2|
因为:|PF1|-|PF2|=2a
解得:|PF1|=8a/3,|PF2|=2a/3
根据余弦定理有:
(2c)^2=(8a/3)^2+(2a/3)^2-2*(8a/3)*(2a/3)*cos∠F1PF2
4c^2=(64/9+4/9)a^2-(32/9)(a^2)*cos∠F1PF2
c^2=[ 17/9-(8/9)*cos∠F1PF2 ]*a^2
e^2=(c/a)^2
=17/9-(8/9)*cos∠F1PF2