5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6b9c61ac-23ec-4346-933f-cf00a2e63695-12_744_697_294_683}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the rectangular hyperbola \(H\) with equation
$$x y = c ^ { 2 } \quad x > 0$$
where \(c\) is a positive constant.
The point \(P \left( c t , \frac { c } { t } \right)\) lies on \(H\).
The line \(l\) is the tangent to \(H\) at the point \(P\).
The line \(l\) crosses the \(x\)-axis at the point \(A\) and crosses the \(y\)-axis at the point \(B\).
The region \(R\), shown shaded in Figure 2, is bounded by the \(x\)-axis, the \(y\)-axis and the line \(l\).
Given that the length \(O B\) is twice the length of \(O A\), where \(O\) is the origin, and that the area of \(R\) is 32 , find the exact coordinates of the point \(P\).