(1) 见图
(2) C(m-2, n), P(m-2, n + 2)
A在双曲线上: mn = k
P在双曲线上: (m - 2)(n + 2) = k = mn + 2m - 2n - 4 = k + 2m - 2n - 4
m = n + 2
AP斜率: (n + 2 - n)/(m - 2 - m) = -1
AP的解析式:y - n = -(x - m) = -x + n + 2
x = 0, y = 2n + 2
E(0, 2n + 2)
△OPE的面积 = (1/2)OE*P的横坐标
= (1/2)(2n + 2)(n + 2 - 2)
= n(n+1) = 2n
n = 1 (舍去n = 0)
m = 3
k = mn = 3
y = 3/x
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