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Math Help - Hyperbola equation solving

  1. #1
    Don
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    Hyperbola equation solving

    Prove that the stright lines x/a - y/b = m and x/a + y/b = 1/m where a and b are given positive real numbers and m is a parameter always meet on a hyperbola.

    No idea how to go about this one. Does this mean that the lines are perpendicular to each other?
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  2. #2
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    Re: Hyperbola equation solving

    Quote Originally Posted by Don View Post
    Prove that the stright lines x/a - y/b = m and x/a + y/b = 1/m where a and b are given positive real numbers and m is a parameter always meet on a hyperbola.

    No idea how to go about this one. Does this mean that the lines are perpendicular to each other?
    1. Eliminate the parameter m: Plug in the LHS of the 1st equation into the 2nd equation:

    \frac xa + \frac yb = \frac1{\frac xa - \frac yb}

    2. Multiply both sides by \left( \frac xa - \frac yb \right) . You'll get

    \displaystyle{\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1}

    which is the equation of a hyperpola with it's center at the origin.
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    Don
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    Re: Hyperbola equation solving

    Thanks.
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