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 : - Clay6.com, a Free resource for your JEE, AIPMT and Board Exam preparation

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 :