Question

Prove that the locus of a point which is equidistant to $x$-axis and $y$-axis is $x=\pm y$

Answer 1

Let $(h,k)$ be the point.

Now distance of the point from the $y$-axiis is $|h|$.

Again the distance of the point from the $x$-axiis is $|k|$.

According to the problem,

$|h|=|k|$

or, $h=\pm k$.

So locus of the point be $x=\pm y$.