The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points $\;(a^{2}+1,a^{2}+1)\;$ and $\;(2a ,-2a)\;, a \neq 0\;$.Then for any a , the orthocentre of this triangle lies on the line :

Question

$(a)\;y-2ax=0\qquad(b)\;y-(a^{2}+1)x=0\qquad(c)\;y+x=0\qquad(d)\;(a-1)^{2}x-(a+1)^{2}y=0$