Locus of Centroid in Parabolic Triangle

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