9758/2020/P2/Q03

The curve $C$ is defined by the parametric equations

$x=3 t^{2}+2, \quad y=6 t-1 \quad \text { where } t \geqslant \frac{1}{6} .$

The line $N$ is the normal to $C$ at the point $(14,11)$.

(i) Find the cartesian equation of $N$. Give your answer in the form $a x+b y=c$, where $a, b$ and $c$ are integers to be determined.

[5]

(ii) Find the area enclosed by $C, N$ and the $x$-axis.

[4]

(iii) The curve $C$ and the line $N$ are both transformed by a 2-way stretch, scale factor 2 in the $x$-direction and scale factor 3 in the $y$-direction, to form the curve $D$ and the line $M$.

(a) Find the area enclosed by $D, M$ and the $x$-axis.

[1]

(b) Find the cartesian equation of $D$.

[2]