Find the focus of the intersection of the lines $\displaystyle \frac{x}{3} - \frac{y}{2} = m $ and $\displaystyle \frac{x}{3} + \frac{y}{2} = m^{-1} $ if m is variable
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Replace m in the second equation: $\displaystyle \frac{x}{3}+\frac{y}{2}=\frac{1}{\frac{x}{3}-\frac{y}{2}}\Rightarrow \frac{x^2}{9}-\frac{y^2}{4}=1$ The locus is a hyperbola.
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