Parabola Problem

Geometry Level 4

From a point $P \ (\alpha,\alpha)$ , tangents are drawn to the parabola $y^2=4ax$ . They touch the parabola in $A$ and $B$ . $\triangle PAB$ is completed. Then the locus of the orthocenter of this triangle is a

$\textbf{Note :} \ \alpha \in \mathbb{R}-[0,4a] \ \text{and} \ a \in \mathbb{R}^+$