(2012?成都)如图,在平面直角坐标系xOy中,直线AB与x轴、y轴分别交于点A,B,与反比例函数y=kx(k为常

2025-05-20 05:43:06
推荐回答(1个)
回答(1):

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=
1
2
(mx-x)(my-y)=
1
2
(m-1)2xy,
∵△OEF的面积为:S2=S矩形CNOM-S1-S△MEO-S△FON
=MC?CN-
1
2
(m-1)2xy-
1
2
ME?MO-
1
2
FN?NO,
=mx?my-
1
2
(m-1)2xy-
1
2
x?my-
1
2
y?mx,
=m2xy-
1
2
(m-1)2xy-mxy,
=
1
2
(m2-1)xy,
=
1
2
(m+1)(m-1)xy,
S1
S2
=
1
2
(m?1) 2xy
1
2
(m?1)(m+1)xy
=
m?1
m+1

故答案为:
m?1
m+1