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Homework Help: Equation of A Hyperbola

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Find an equation of the hyperbola with it's center at the origin.

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

    2. Relevant equations
    Equation for the asymptotes of a hyperbola with a horizontal transverse axis
    [tex]y=k\pm\frac{b}{a}(x-h)[/tex]

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

    [tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]

    3. 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 [tex]a^2+b^2=64[/tex] and from looking at the asymptotes I can also declare that [tex]\frac{b}{a}=4[/tex]. I dont know how to solve a system of equations with division in it. Is there something I am missing?
     
  2. jcsd
  3. Jul 15, 2010 #2

    LCKurtz

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    Put b = 4a from the second equation in the first equation and solve for a. Then solve for b.
     
  4. Jul 16, 2010 #3
    Ahh.. Yes.

    Thanks!
     
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