16.
\section*{Figure 3}
\includegraphics[max width=\textwidth, alt={}]{b85f4635-aa93-4c6a-9d1f-2ef5bac1b48c-08_581_575_395_609}
The points \(A ( - 3 , - 2 )\) and \(B ( 8,4 )\) are at the ends of a diameter of the circle shown in Fig. 3.
- Find the coordinates of the centre of the circle.
- Find an equation of the diameter \(A B\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
- Find an equation of tangent to the circle at \(B\).
The line \(l\) passes through \(A\) and the origin.
- Find the coordinates of the point at which \(l\) intersects the tangent to the circle at \(B\), giving your answer as exact fractions.