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Math Help - [SOLVED] finding hyperbolic equations

  1. #1
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    [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.
    Last edited by satis; March 28th 2010 at 11:56 AM.
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    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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