Parabola

Let $\mathrm{A}, \mathrm{B}$ and C be the vertices of a variable right angled triangle inscribed in the parabola $y^2=16 x$. Let the vertex $B$ containing the right angle be $(4,8)$ and the locus of the centroid of $\triangle A B C$ be a conic $C_0$. Then three times the length of latus rectum of $\mathrm{C}_0$ is $\_\_\_\_$