[SOLVED] finding hyperbolic equations

**satis** · March 28th 2010, 11:38 AM

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.

**HallsofIvy** · March 28th 2010, 01:08 PM

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.

**satis** · March 29th 2010, 06:28 AM

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.

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