Find the equation of the set of all points the sum of whose distances from the points $(3, 0)$ and $(9, 0)$ is 12.

Question

$\begin{array}{1 1}3x^2+4y^2+36x=0\\3x^2-4y^2+36x=0\\3x^2+4y^2-36x=0\\3x^2-4y^2-36x=0\end{array}$