A curve $C$ has parametric equations $x = t^2 + t$, $y = t^2 - t$, $t \in \mathbb{R}$. Sketc

Question

A curve $C$ has parametric equations $x = t^2 + t$, $y = t^2 - t$, $t \in \mathbb{R}$. Sketch the graph of $C$, indicating the coordinates of the points where the curve crosses either axis.[2] Find the coordinates of the point on $C$ where the tangent to $C$ is parallel to the line $5y = 4x - 20$.[3] Find the equation of the tangent to $C$ at the point $(0, 2)$ and show algebraically that this tangent does not cut $C$ again.[5]

Accepted Answer

(i) Axis crossings: $(0,0)$, $(0,2)$ and $(2,0)$. (ii) $\left(\dfrac{99}{4},\dfrac{63}{4}\right)$. (iii) $y=3x+2$; substitution gives only the double root $t=-1$, so the tangent does not cut $C$ again.

2024 JPJC Promo Q10

2024 JPJC Promo Q10

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