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
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