Normals are drawn from the point $P$ with slopes $m_{1},m_{2},m_{3}$ to the parabola $y² = 4 x$. If locus of $P$ with $m_{1}m_{2}= \alpha$ is a part of parabola itself, find the value of $\alpha$.

This one is blast from past. Question is from IIT JEE 2003.

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