Let $^{\rm{n}}{{\rm{C}}_{{\rm{r}} - 1}} = 28{,^{\rm{n}}}{{\rm{C}}_{\rm{r}}} = 56$ and $^{\rm{n}}{{\rm{C}}_{{\rm{r}} + 1}} = 70$. Let ${\rm{A}}(4{\mathop{\rm cost}\nolimits} ,4\sin {\rm{t}}),{\rm{B}}(2\sin {\rm{t}}, - 2\cos {\rm{t}})$ and ${\rm{C}}\left( {3{\rm{r}} - {\rm{n}},{{\rm{r}}^2} - {\rm{n}} - 1} \right)$ be the vertices of a triangle ABC , where t is a parameter. If ${(3{\rm{x}} - 1)^2} + {(3y)^2}$ $=\alpha$, is the locus of the centroid of triangle ABC, then $\alpha$ equals