How to solve the part between the red lines: Show that the eqn of the locus of the point of....

[AleksandrB]

 

[stapel]

11. If the normal at $P(ap^2,\, 2ab)$ to the parabola $y^2 = 4ax$ meets the curve again at $Q(aq^2, 2aq)$, show that $p^2 + pq + 2 = 0$. $\color{red}{\blacktriangleright}$Show that the equation of the locus of the point of intersection of the tangents at $P$ and $Q$ to the parabola is $y^2 (x + 2a) + 4a^3 = 0$.$\color{red}\blacktriangleleft$

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