TP and TQ are tangents to parabola $y^2=8x$ and normal at P and Q intersect at a point R on the parabola. The locus of circumcentre of $\Delta TPQ$ is a parabola whose

$t_1{t}_2=2and{t}_1+t_2=-t^{3}anda=2$

Let circumcentre of $\Delta TPQ$ be $O(h,k)$

$O(h,k)$  will be midpoint of RT $(\therefore \angle P=\angle Q={90}^0)$
$$\begin{gathered} h=\frac{a{t}_1{t}_2+a{t}_3^2}{2}\Rightarrow h=2+t_3^2\mathrm{................}\left(1\right) \\ and k=\frac{a(t_1+t_2)+2a{t}_3}{2}\Rightarrow k=t_3\mathrm{................}\left(2\right) \\ h=2+k^2 \\ Locus of O(h,k)is \\ \Rightarrow O(h,k) \\ {y}^2=x-2 \\ {y}^2=1(x-2) \end{gathered}$$