The curve $C$ has parametric equations $x={{t}^{2}}+2$ , $y={{t}^{3}}$ where $t\in \mathbb{R}$. Sket

Question

The curve $C$ has parametric equations $x={{t}^{2}}+2$ , $y={{t}^{3}}$ where $t\in \mathbb{R}$. Sketch the curve $C$. [1] The tangent to the curve at point $P$ where $t=2$ is denoted by $l$. Find the Cartesian equation of $l$. [3] The tangent $l$ meets $C$ again at point $Q$. Use a non-calculator method to show that the coordinates of $Q$ is $\left( 3,-1 \right)$. [4]

Accepted Answer

(i) $y^2=(x-2)^3$, with cusp $(2,0)$ (ii) $l:y=3x-10$ (iii) $Q=(3,-1)$

2013 CJC P1 Q11

2013 CJC P1 Q11

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