由题设知,F),1(-c,0),B(0,b),A(a,0).
过F(-c,0)和B(0,b)两点的直线方程为:(y-0)/(b-0)=[x-(-c)]./[0-(-c)]
化简,得:bx-cy+bc=0.∵c0,约去b,得:
|a-c|=√[(b^2+c^2)/7],两边平方,得:
|a-c|^2=(b^2+c^2)/7.
a^2-2ac+c^2=(b^2+c^2)/7.
7a^2-14ac+7c^2=b^2+c^2.
各项同除以a^2,得:
7-14c/a+7c^2/a^2=b^2/a^2+c^2/a^2.【b^2/a^2=c^2/a^2-1】.
7-14e+7e^2=e^2-1+e^2.
5e^2-14e+8=0.
( 5e-4)(e-2)=0.
5e-4=0,e=4/5