How do I find the equation of a hyperbola with given foci and asymptotes?

[themadhatter1]

Homework Statement

Find an equation of the hyperbola with it's center at the origin.

Foci:(8,0),(-8,0) Asymptotes: y=4x, y=-4x

Homework Equations

Equation for the asymptotes of a hyperbola with a horizontal transverse axis
$$y=k\pm\frac{b}{a}(x-h)$$

Equation for a hyperbola centered at (0,0) and having a horizontal transverse axis in standard form

$$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$

The Attempt at a Solution

Ok, so I need to find a and b to write the equation.

I can deduce from the information given that c=8 which is the distance from the center to a focus.

Therefore I can declare that $$a^2+b^2=64$$ and from looking at the asymptotes I can also declare that $$\frac{b}{a}=4$$. I don't know how to solve a system of equations with division in it. Is there something I am missing?

 

[LCKurtz]

Put b = 4a from the second equation in the first equation and solve for a. Then solve for b.

 

[themadhatter1]

Put b = 4a from the second equation in the first equation and solve for a. Then solve for b.

Ahh.. Yes.

Thanks!