設(shè)P(x,y)
PF1與PF2的數(shù)量積=（x+c,y)(x-c,y)=x^2-c^2+y^2
由x^2/a^2-y^2/b^2=1得
y^2=x^2*b^2/a^2-b^2
帶入上式,再將b^2=c^2-a^2帶入得：
數(shù)量積=c^2/a^2*x^2+a^2-2c^2
(設(shè)數(shù)量積等于t)
又c=ea,
t=e^2*x^2+a^2-2e^2*a^2
移項(xiàng)
x^2=(t+2e^2*a^2-a^2)/e^2
對(duì)雙曲線上任意一點(diǎn)：x^2>=a^2
即：(t+2e^2*a^2-a^2)/e^2>=a^2
整理：
e^2*a^2>=a^2-t
e^2>=1-t/a^2
t:[-3a^2,-a^2]
-t/a^2:[1,3]
e^2>=2
e>=根號(hào)2