A curve $C$ has parametric equations $x=a\left( {{t}^{2}}-t \right)$, \(y=a\left( 1-2{{t}^{2}} \

Question

A curve $C$ has parametric equations $x=a\left( {{t}^{2}}-t \right)$, $y=a\left( 1-2{{t}^{2}} \right)$, $-3 < t\le 2$, where $a$ is a positive constant. Sketch the graph of $C$, stating the coordinates of the end-points.[2] Find, in terms of $a$, the equation of the normal at the point where $t=-1$.[4] the exact coordinates of the point where the normal cuts $C$ again.[4]

Accepted Answer

(a) $\left( 2a,-7a \right)$ and $\left( 12a,-17a \right)$. (b)(i) $y=\frac{3}{4}x-\frac{5}{2}a$ (ii) $\left( \frac{42}{121}a,\ -\frac{271}{121}a \right)$

2024 YIJC Promo Q6

2024 YIJC Promo Q6

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