This problem has been bothering me for a while.

Given the two asymptotes y = 2x and y = -2x + 4, and a random point on the hyperbola (0,6), find the equation of the hyperbola.

So I've found out that the center would be (1,2) and that the hyperbola would be horizontally oriented. But now I'm stuck on how to use (0,6) to establish the equation.

Any help please? Thanks.