The curve $C$ is defined by the parametric equations $x=3{{t}^{2}}+2$, $y=6t-1$ where $t\ge \frac{1}

Question

The curve $C$ is defined by the parametric equations $x=3{{t}^{2}}+2$, $y=6t-1$ where $t\ge \frac{1}{6}$. The line $N$ is the normal to $C$ at the point $\left( 14,\,\,11 \right)$. Find the cartesian equation of $N$. Give your answer in the form $ax+by=c$, where $a$, $b$ and $c$ are integers to be determined. [5] Find the area enclosed by $C$, $N$ and the $x$-axis. [4] The curve $C$ and the line $N$ are both transformed by a $2$-way stretch, scale factor $2$ in the $x$-direction and scare factor $3$ in the $y$-direction, to form the curve $D$ and the line $M$. Find the area enclosed by $D$,$M$ and the $x$-axis. [1] Find the cartesian equation of $D$. [2]

Accepted Answer

(i) $2x + y = 39$ (ii) $\frac{2057}{18}$ units$^2$ (iii)(a) $\frac{2057}{3}$ units$^2$ (iii)(b) $54x = y^2 + 6y + 225$

N2020 P2 Q3

N2020 P2 Q3

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