5
- 1
\end{array} \right)$$
where \(a\) is a constant.
Given that \(\overrightarrow { O C }\) is perpendicular to \(\overrightarrow { B C }\)
(b) find the possible values of \(a\).
- The curve \(C\) is defined by the equation
$$8 x ^ { 3 } - 3 y ^ { 2 } + 2 x y = 9$$
Find an equation of the normal to \(C\) at the point ( 2,5 ), giving your answer in the form \(a x + b y + c = 0\), where \(a\), \(b\) and \(c\) are integers.
4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e583bf92-d6a9-4f1a-b3c8-372afa6e0a0e-08_558_542_258_749}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of a segment \(P Q R P\) of a circle with centre \(O\) and radius 5 cm .
Given that
\begin{itemize}
\item angle \(P O R\) is \(\theta\) radians
\item \(\theta\) is increasing, from 0 to \(\pi\), at a constant rate of 0.1 radians per second
\item the area of the segment \(P Q R P\) is \(A \mathrm {~cm} ^ { 2 }\)