A curve $C$ has parametric equations $x={{t}^{2}}-4t$, $y={{t}^{3}}-6t$. Using calculus, find

Question

A curve $C$ has parametric equations $x={{t}^{2}}-4t$, $y={{t}^{3}}-6t$. Using calculus, find the equation of the normal at the point $P$ where $t=1$.[4] The normal at $P$ meets the curve again at two other points. Show that $t$ satisfies the equation $3{{t}^{3}}+2{{t}^{2}}-26t+21=0$ at these two points and hence find the coordinates of the points.[3]

Accepted Answer

(a) ${y = -\frac{2}{3}x - 7}$ (b) The coordinates of the points are ${(27.4, -25.3)}$ and ${(-4.00, -4.34)}$ ($3$ s.f)

2023 YIJC Promo Q7

2023 YIJC Promo Q7

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