Locus of centroid of the triangle whose vertices are $( a \cos t, \; a \sin t), \; (b \sin t, -b \cos t)$ and $(1, 0)$ where $t$ is a parameter, is :

Question

( A ) $(3x-1)^2 + (3y)^2 = a^2 - b^2$
( B ) $(3x+1)^2 + (3y)^2 = a^2 + b^2$
( C ) $(3x-1)^2 + (3y)^2 = a^2 + b^2$
( D ) $(3x+1)^2 + (3y)^2 = a^2 - b^2$