The ordinate of the centroid of the triangle formed by conormal points on the parabola   $y^2=4ax$ is

Equation of the normal at t is $y+xt=2at+a{t}^3$

$t_1+t_2+t_3=0$

The ordinate of the centroid of the triangle at is   $t_1,t_2,t_3$   is  $\frac{2a{t}_1+2a{t}_2+2a{t}_3}{3}$

$\frac{2a}{3}\left(t_1+t_2+t_3\right)=0$