Could you please help with this locus problem? I think I am aiming for a cartesian equation in terms of $x$ and $y$ that may look like a circle equation e.g. $(x+a)^2 + (y+b)^2$ but I'm not sure.
Given there is a locus of $z$ such that $\frac{|z-12j|}{|z+36|}=3,$ then $|z-12j| = 3|z+36|$.
Now I want to write the locus of $z$ as a cartesian equation in terms of $x$ and $y$. Let $z=x+yj$. $\begin{align*} |x+yj - 12j| &= 3|x+yj+36|\\ |x+(y-12)j| &= 3|(x+36)+yj| \end{align*}$ Where should I go from here?