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Math Help - Find the locus of interestion of the lines

  1. #1
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    Find the locus of interestion of the lines

    Find the focus of the intersection of the lines

    <br />
\frac{x}{3} - \frac{y}{2} = m<br />
and <br />
\frac{x}{3} + \frac{y}{2} = m^{-1}<br />
if m is variable
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  2. #2
    MHF Contributor red_dog's Avatar
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    Replace m in the second equation:

    \frac{x}{3}+\frac{y}{2}=\frac{1}{\frac{x}{3}-\frac{y}{2}}\Rightarrow \frac{x^2}{9}-\frac{y^2}{4}=1

    The locus is a hyperbola.
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