Thread: Find the locus of interestion of the lines

1. Find the locus of interestion of the lines

Find the focus of the intersection of the lines

$
\frac{x}{3} - \frac{y}{2} = m
$
and $
\frac{x}{3} + \frac{y}{2} = m^{-1}
$
if m is variable

2. 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.