已知点A,B,F分别为椭圆C：x^2/a^2+y^2/b^2=1（a>b>0）的右顶点、上顶点和左焦距,直线l的方程为x=a2/c,

设MN与x交于H
OB/MH = OF/FH → MH = b*(c+a^2/c)/c = b(1+1/e^2)
OB/NH = OA/AH → NH = b*(a^2/c-a)/a = b( 1/e-1)
MN = MH+NH = b(1+1/e^2-1+1/e) =4b
(1/e)^2+1/e =4 (1/e>1)
1/e=（-1+√17）/2
e = 2/（-1+√17）= （+1+√17）/8