Question

Write the coordinates of a point on each of the axes such that they are equidistant from the orgin

Answer 1

Assumed points :-

$A ( x,y)$

$O(0,0)$

$B(p,q)$

AO = OB

$\sqrt{p^2+q^2} =\sqrt{x^2+y^2}$

$p^2+q^2=x^2+y^2$

This is the locus of the situation you wanted.