解答:解:过点F作FD⊥BO于点D,EW⊥AO于点W,
∵
=BE BF
,1 m
∴
=ME DF
,1 m
∵ME?EW=FN?DF,
∴
=ME DF
,FN EW
∴
=FN EW
,1 m
设E点坐标为:(x,my),则F点坐标为:(mx,y),
∴△CEF的面积为:S1=
(mx-x)(my-y)=1 2
(m-1)2xy,1 2
∵△OEF的面积为:S2=S矩形CNOM-S1-S△MEO-S△FON,
=MC?CN-
(m-1)2xy-1 2
ME?MO-1 2
FN?NO,1 2
=mx?my-
(m-1)2xy-1 2
x?my-1 2
y?mx,1 2
=m2xy-
(m-1)2xy-mxy,1 2
=
(m2-1)xy,1 2
=
(m+1)(m-1)xy,1 2
∴
=S1 S2
=
(m?1) 2xy1 2
(m?1)(m+1)xy1 2
.m?1 m+1
故答案为:
.m?1 m+1