The circumcentre of a triangle lies at the origin and the centroid is the midpoint of the line segment joining the points a2+1,a2+1 and (2a,−2a) , then the orthocentre lies on the line.

We know that, circumcentre, centroid and orthocentre of a triangle are collinear.Hence, orthocentre lies on the line joining circumcentre (0, 0) and centroid   (a+1)22,(a−1)22Equation of the line is (a+1)22y=(a−1)22x(a−1)2x−(a+1)2y=0Therefore, the equation of the line where the orthocentre lies is  (a−1)2x−(a+1)2y=0