5.
\section*{Figure 1}
\includegraphics[max width=\textwidth, alt={}]{3d5491ef-91cf-4ba9-b00b-cd326d51e6e1-3_686_1066_276_559}
Figure 1 shows the curve with equation \(y ^ { 2 } = 4 ( x - 2 )\) and the line with equation \(2 x - 3 y = 12\).
The curve crosses the \(x\)-axis at the point \(A\), and the line intersects the curve at the points \(P\) and \(Q\).
- Write down the coordinates of \(A\).
- Find, using algebra, the coordinates of \(P\) and \(Q\).
- Show that \(\angle P A Q\) is a right angle.
\begin{figure}[h]
\captionsetup{labelformat=empty}
\caption{Figure 2}
\includegraphics[alt={},max width=\textwidth]{3d5491ef-91cf-4ba9-b00b-cd326d51e6e1-4_646_1043_291_336}
\end{figure}
The points \(A ( 3,0 )\) and \(B ( 0,4 )\) are two vertices of the rectangle \(A B C D\), as shown in Fig. 2.