x^2/a^2-y^2/b^2=1
2a+2b=2
b=1-a
F1F2=2根号(a^2+b^2)
=2根号[a^2+(1-a)^2]
=2根号[2a^2-2a+1]
=2根号[2(a-1/2)^2+3/2] ≥ 2根号(3/2) = 根号6