9 The curve $C$ has polar equation

$$r = 5 \sqrt { } ( \cot \theta ) ,$$

where $0.01 \leqslant \theta \leqslant \frac { 1 } { 2 } \pi$.\\
(i) Find the area of the finite region bounded by $C$ and the line $\theta = 0.01$, showing full working. Give your answer correct to 1 decimal place.\\

Let $P$ be the point on $C$ where $\theta = 0.01$.\\
(ii) Find the distance of $P$ from the initial line, giving your answer correct to 1 decimal place.\\

(iii) Find the maximum distance of $C$ from the initial line.\\

(iv) Sketch $C$.

\hfill \mbox{\textit{CAIE FP1 2018 Q9}}