Let \( {}^nC_{r-1} = 28 \), \( {}^nC_r = 56 \) and \( {}^nC_{r+1} = 70 \).
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 \( r \) is a parameter. If \( (3x - 1)^2 + (3y)^2 = \alpha \), is the locus of the centroid of triangle \( ABC \), then \( \alpha \) equals:
