A(8,0),B(0,6)
△AOB面积S = (1/2)OA*OB = (1/2)*8*6 = 24
两部分面积比是1:5,则较小的部分面积为24*1/(1 + 5) = 4,较大的部分面积为20
y=kx+b过点C(4,0):4k + b = 0,b = -4k
y = k(x - 4)
与y = -3x/4 + 6的交点为D(8(2k + 3)/(4k + 3),12k/(4k + 3))
(1) 当D在线段AB上时
(i) 较小的部分面积为△ACD面积 = (1/2)CA*D的纵坐标
= (1/2)(8 - 4)*12k/(4k + 3) = 4
k = 3/2
过点C的直线解析式:y = 3(x - 4)/2
(ii) 较大的部分面积为△ACD面积 = (1/2)CA*D的纵坐标
= (1/2)(8 - 4)*12k/(4k + 3) = 20
k = -15/14
D的纵坐标 < 0,舍去
(2)D不在线段AB上,过点C的直线与y轴的交点为E(0,-4k)
(i) 较小的部分面积为△OCE面积 = (1/2)OC*E的纵坐标
= (1/2)(4- 0)(-4k) = -8k = 4
k = -1/2,E(0,2)在线段OA上,过点C的直线解析式:y = 2 - x/2
(ii)较小的部分面积为△OCE面积 = (1/2)OC*E的纵坐标
= (1/2)(4- 0)(-4k) = -8k = 20
k = -5/2,E(0,10)不在线段OA上,舍去