Let A, 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…

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