(1)解析：∵直线y=4/3x-4交y轴于点A,交x轴于点B,交双曲线y=a/x于点D
a/x=4/3x-4?4x^2-12x-3a=0==>x1=[3-√(9+3a)]/2,x2=[3+√(9+3a)]/2
y1=a/[3-√(9+3a)]/2= 2a/[3-√(9+3a)] = -2[3+√(9+3a)]/3
y1=a/[3+√(9+3a)]/2= 2a/[3+√(9+3a)] = -2[3-√(9+3a)]/3
当a>0时
与双曲线交点在第三象限,则CD= -2[3+√(9+3a)]/3
与双曲线交点在第一象限,则CD= -2[3-√(9+3a)]/3
当-3a>=-3