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

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