The normal at the point \( \mathrm{P}\left(\mathrm{ap}^{2}, 2 \mathrm{ap}\right) \) meets the pa...

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The normal at the point \( \mathrm{P}\left(\mathrm{ap}^{2}, 2 \mathrm{ap}\right) \) meets the parabola \( \mathrm{y}^{2}=4 \mathrm{ax} \) again at \( \mathrm{Q}\left(\mathrm{aq}^{2}, 2 \mathrm{aq}\right) \) such that the lines joining the origin to \( \mathrm{P} \) and \( \mathrm{Q} \) are at right angle. Then prove that \( \mathrm{p}^{2}=2 \).
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