A curve $C$ is defined parametrically by $x=6t,\ y=t^2$. Show that the equation of the normal at

Question

A curve $C$ is defined parametrically by $x=6t,\ y=t^2$. Show that the equation of the normal at the point $P(6p, p^2)$ is $p^3+(18-y)p-3x=0$.[3] The normal to the curve at the point $P$ meets the curve again at the point $Q(-54,81)$. Find the possible values of $p$.[2] Sketch the graph of $C$, indicating clearly the coordinates of $Q$ and the possible points of $P$. Sketch also the normals at each of these points $P$.[3]

Accepted Answer

(b) $p=3$ or $6$ (c) $P=(18,9)$ or $(36,36)$, with $Q=(-54,81)$

2025 EJC Promo Q6

2025 EJC Promo Q6

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