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