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Math Help - need help with hyperbola equations

  1. #1
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    May 2009
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    need help with hyperbola equations

    I am having issues with finding hyperbola equations with a translation when it gives the vertices and foci.
    vertices: (-5,5) (5,5)
    foci: (-7,5) (7,5)
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  2. #2
    Super Member
    Joined
    May 2009
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    The focal axis is horizontal, so the equation is in the form
    \frac{(x - h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1

    The center (h, k) is in between the two vertices, so it's (0, 5).
    a is the distance from the center to one of the vertices, so a = 5.
    c is the distance from the center to one of the foci, so c = 7.
    The relationship between a, b, c is
    c^2 = a^2 + b^2
    so solve for b:
    7^2 = 5^2 + b^2
    49 = 25 + b^2
    24 = b^2
    b = \sqrt{24}

    So the equation should be
    \frac{x^2}{25} - \frac{(y - 5)^2}{24} = 1
    Nothing to it!


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