1. ## Hyperbola help

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.

2. Originally Posted by Chis
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.

refer to post #2 here

note that b/a = 2, that is, b = 2a

you also know the values of h and k, and you are given x and y values, namely, x = 0 and y = 6. you can plug in all these values into the standard form (writing b as 2a) and thus solve for a. then you can find b and then you can find the equation you want