x^2/a^2-y^2=1
PF1^2/PF2>=8a
PF1^2/(PF1-2a)>=8a
PF1^2-8aPF1+16a^2>=0
(PF1-4a)^2>=0
PF1最小时,PF1=√(a^2+1)+a
4a=√(a^2+1)+a
8a^2=1
a=1/2√2
因此a==0,PF1^2/PF2最小值8
实轴长2a>=1/√2