设|PF1|=r1,|PF1|=r2,
1/2r1r2sin60度=12根号下3
|r1-r2 |=2a
r1^2+r2^2-2r1r2cos60度=(2c)^2
消r1,r2
r1r2=48,r1^2+r2^2-2r1r2=4a^2 r1^2+r2^2-r1r2=4c^2
后两个式子相减
4c^2-4a^2=r1r2=48
c^2-a^2=b^2
b=4
e=2.设c=2k,a=k
k=4/√3
a=4/√3
双曲线的方程有两个:
3x^2/16-y^2/16=1
3y^2/16-x^2/16=1