Two long straight conductors with currents $I_1$ and $I_2$ are placed along $X$ and $Y-$ axes. The equation of locus of points of zero magnetic induction is
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magnetic field $B=\frac{\mu_{0} I}{2 \pi r}$
the magnetic field at any point in the $xy$ plane $B=\frac{\mu_{0} I_{1}}{2 \pi y}-\frac{\mu_{0} I_{2}}{2 \pi x}$
(assuming current flowing in $x$ and $y$$-direction$ respectively.)
So, the equation of the locus of zero magnetic induction,
$\frac{I_{1}}{y}=\frac{I_{2}}{x}$
$y=\frac{I_{1} x}{I_{2}}$
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