Let \({}^{n}C_{r-1}=28,{}^{n}C_{r}=56\) and \({}^{n}C_{r+1}=70\), let \(A(4cost,4\sin t)\), \(B(2\sin t,-2cost)\) and \(…

Let \({}^{n}C_{r-1}=28,{}^{n}C_{r}=56\) and \({}^{n}C_{r+1}=70\), let \(A(4cost,4\sin t)\), \(B(2\sin t,-2cost)\) and \(C\left(3r-n,{r}^{2}-n-1\right)\) be the vertices of a triangles ABC, where \(t\) is a parameter. If \((3x-1{)}^{2}+(3y{)}^{2}=\alpha\), is the locus of the centroid of triangle ABC , then \(\alpha\) equates. (28 Jan, Shift I, Memory Based)