The normal at a point \( \mathrm{P} \) to the parabola \( \mathrm{y...

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The normal at a point \( \mathrm{P} \) to the parabola \( \mathrm{y}^{2}=4 a x \) meets its axis at \( \mathrm{G} \). \( \mathrm{Q} \) is another point on the parabola
\( \mathrm{P} \) such that \( \mathrm{QG} \) is perpendicular to the axis of the parabola. Prove that \( \mathrm{QG}^{2}-\mathrm{PG}^{2}= \) constant.

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