Question

如图，已知点A，C在反比例函数y=x分之a(a>0)的图象上，点B，D在反比例函数y=x分之b(b

如图，已知点A，C在反比例函数y=x分之a(a>0)的图象上，点B，D在反比例函数y=x分之b(bb<0)的图象上，AB平行CD平行x轴，AB，CD在x轴的两侧，AB=3，CD=2，AB与CD的距离为5，则a-b的值

Answer 1

不妨令A, B在x轴上方，其纵坐标为t > 0, 则A(a/t, t), B(b/t, t)
AB = a/t - b/t = (a - b)/t = 3
t = (a - b)/3

AB与CD的距离为5， 则C,D的纵坐标为t - 5 = (a - b)/3 - 5 = (a - b - 15)/3
C(3a/(a - b - 15), (a - b - 15)/3), D(3b/(a - b - 15), (a - b - 15)/3)
CD = 3b/(a - b - 15) - 3a/(a - b - 15) = -3(a - b)/(a - b - 15) = 2
2(a - b - 15) = -3(a - b)
5(a - b) = 30
a - b = 6