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Math Help - Hyperbola Problem

  1. #1
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    Hyperbola Problem

    (x^2)/25 - (y^2)/(b^2)=1

    Find the directrices, foci, and eccentricity of hyperobola????
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  2. #2
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    Re: Hyperbola Problem

    Quote Originally Posted by aab300 View Post
    (x^2)/25 - (y^2)/(b^2)=1

    Find the directrices, foci, and eccentricity of hyperobola????
    It would be much easier for us to help you if you have shown some work, because this question is quite straight forward.

    Your equation describes a family of hyperbolae with the properties:

    e^2 = a^2+b^2~\implies~e^2=25+b^2

    Thus the foci have the coordinates:

    F_1\left(-\sqrt{25+b^2}, 0  \right) ; F_2\left(\sqrt{25+b^2}, 0  \right)

    The numerical eccenticity is \epsilon = \frac ea

    and therefore the equation of the directrice is D: x = \epsilon

    Since b > 0 ~\implies~\epsilon > 1
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