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Math Help - Find an equation

  1. #1
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    Find an equation

    Can someone help walk me through this problem? I'd really appreciate your help.

    Find an equation in standard form for the hyperbola with vertices at (0, -10) and asymptotes at y= +-(5/4)x
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Find an equation

    If the transverse axis is on the y-axis, then the form of the hyperbola is:

    \frac{y^2}{a^2}-\frac{x^2}{b^2}=1 where 0<a,b.

    Since the vertices are (presumably) at (0,\pm10), then what is the value of a?

    The asymptotes will be at y=\pm\frac{a}{b}x, so from the given asymptotes, we know:

    \frac{a}{b}=\frac{5}{4}

    b=\frac{4}{5}a

    Use the value you found for a to find b.

    and so what is the equation of the hyperbola?
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  3. #3
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    Re: Find an equation

    Would a be -10?

    Which would make b 8?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Find an equation

    a and b are both positive, so a=10 and yes, then b=8.
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  5. #5
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    Re: Find an equation

    So the equation would just be

    y^2/100 - x^2/64 = 1?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Find an equation

    Yes, although the standard form is:

    \frac{y^2}{10^2}-\frac{x^2}{8^2}=1
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  7. #7
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    Re: Find an equation

    Thank you so much for your help. I really appreciate it.
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