If \( x \cos \alpha+y \sin \alpha=p \), where \( p=-\frac{\sin ^{2} \alpha}{\cos \alpha} \) be a...

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If \( x \cos \alpha+y \sin \alpha=p \), where \( p=-\frac{\sin ^{2} \alpha}{\cos \alpha} \) be a straight line, prove that the perpendiculars on this straight line from the points \( \left(m^{2}, 2 m\right),\left(m m^{\prime}, m+m^{\prime}\right),\left(m^{\prime 2}, 2 m^{\prime}\right) \) form a G.P.
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