(1)
∵双曲线过点(6,1)
∴1 = k/6,k = 6
(2) 设C(c,6/c),c < 0
BD = 6
BD上的高为C的纵坐标的绝对值:-6/c
∴S = (1/2)*BD*(-6/c) = (1/2)*6*(-6/c) = -18/c = 12
c = -3/2,C(-3/2,-4)
∴CD的方程为:(y - 1)/(-4 - 1) = (x - 6)/(-3/2 - 6)
,即y = 2x/3 - 3
(3)
A(-3/2,0)
∴AB斜率=(1 - 0)/(0 + 3/2) = 2/3
∵AB与CD的斜率相等
∴二者平行