Modulus of complex numbers problem draw the loci Given $|z − 3| + |z + 3| = 12$,  $z = x + iy$, find the expression in terms of $x$ and $y$ and draw the loci.
I've tried many ways and I cannot isolate $x$ or $y$. I think that is necessary put the equation in this form $(x-a)^2 + (y-b)^2 = r^2$. 
May someone help me?

If $z=x+iy$ where $x,y$ are real
For
$$\sqrt{(x-c)^2+y^2}+\sqrt{(x+c)^2+y^2}=2a$$
$$(x+c)^2+y^2=4a^2+(x-c)^2+y^2-4a\sqrt{(x-c)^2+y^2}$$
$$\iff a\sqrt{(x-c)^2+y^2}=a^2-cx$$
Squaring we get  $$a^2\{(x-c)^2+y^2\}=a^4-2a^2cx+c^2x^2$$
$$\iff(a^2-c^2)x^2+a^2y^2=a^2(a^2-c^2)$$
For $a\ne c,$  $$\dfrac{x^2}{a^2}+\dfrac{y^2}{a^2-c^2}=1$$
