# Thread: [SOLVED] finding hyperbolic equations

1. ## [SOLVED] finding hyperbolic equations

mostly these are pretty easy to figure out, but I'm confused on this one.

Given the following, find the standard equation of the hyperbola

foci: (0, +/-8)
asymptotes: y=+/-4x

From the foci, I know the origin is at 0,0 and that it's vertical, which gives me
$\frac{y^2}{a^2} - \frac{x^2}{b^2}$

I also know that $c^2 = a^2 + b^2$, and, from the asymptote, I know that the ratio of rise to run is 4:1, so a=4b

I'm not really sure how to proceed from here, though. Can someone point me in the right direction please?

*edit*
forgot to add that, from the foci, I know that c=8. Still not sure how to proceed.

2. Yes, you know that a= 4b and that $c^2= a^2+ b^2= 8^2= 64$. Replace a in $a^2+ b^2= 64$ by 4b and you will have a simple equation for b.

3. Originally Posted by HallsofIvy
Yes, you know that a= 4b and that $c^2= a^2+ b^2= 8^2= 64$. Replace a in $a^2+ b^2= 64$ by 4b and you will have a simple equation for b.
Thanks... I knew I had all the elements needed to solve the problem, but for some reason I couldn't figure out how to put everything together properly. I appreciate the assistance.