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

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

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