13 Figure 2 shows the approximate shape of the vertical cross section of the entrance to a cave. The cave has a horizontal floor.
The entrance to the cave joins the floor at the points \(O\) and \(P\).
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{22ff390e-1360-43bd-8c7f-3d2b58627e91-24_396_991_584_529}
\end{figure}
Garry models the shape of the cross section of the entrance to the cave using the equation
$$x ^ { 2 } + y ^ { 2 } = a \sqrt { x } - y$$
where \(a\) is a constant, and \(x\) and \(y\) are the horizontal and vertical distances respectively, in metres, measured from \(O\).
13
- The distance \(O P\) is 16 metres.
Find the value of \(a\) that Garry should use in the model.
\includegraphics[max width=\textwidth, alt={}, center]{22ff390e-1360-43bd-8c7f-3d2b58627e91-25_2518_1723_196_148}