If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the line joining the points (a2+1, a2+1) and (2a, –2a); then the orthocentre lies on the line

We know from geometry that the circumcentre, centroid and orthocentre of a triangle lie on a line. So the orthocentre of the triangle lies on the line joining the circumcentre (0, 0) and the centroid (a+1)22,(a−1)22 i.e. (a+1)22y=(a−1)22xor (a−1)2x−(a+1)2y=0.