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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?

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    Square both sides and use the fact that $|a+bj|^2 = a^2 + b^2$, then simplify.2012-05-28
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    You can type equations directly, instead of creating images and then linking to them. In fact, it's better not to rely on images.2012-05-28
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    Thanks @ArturoMagidin I'd like to learn how to type equations, is there some instructions for that somewhere on here?2012-05-28
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    @NSDigital: [This](http://meta.math.stackexchange.com/q/1773/742) should get you started.2012-05-28
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    Note: $(x+a)^2 + (y+b)^2$ is not an equation. A dead giveaway that it is not an equation is the fact that it does not have an equal sign in it.2012-05-29

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