7.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{922202a6-3455-433f-ac8f-673daefaa7d2-3_574_574_879_662}
\end{figure}
The points \(A ( - 3 , - 2 )\) and \(B ( 8,4 )\) are at the ends of a diameter of the circle shown in Fig. 1.
- 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.