Find the equation of the set of all points whose distance from $(0, 4)$ are $\large\frac{2}{3}$ of their distance from the line $y = 9$.

Question

$\begin{array}{1 1}5x^2-5y^2+180=0\\5x^2-5y^2-180=0\\5x^2+5y^2+180=0\\5x^2+5y^2-180=0\end{array}$