6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{59c9f675-e7eb-47b9-b233-dfbe1844f792-18_579_620_219_667}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The points \(P ( 23,14 ) , Q ( 15 , - 30 )\) and \(R ( - 7 , - 26 )\) lie on the circle \(C\), as shown in Figure 1.
- Show that angle \(P Q R = 90 ^ { \circ }\)
- Hence, or otherwise, find
- the centre of \(C\),
- the radius of \(C\).
Given that the point \(S\) lies on \(C\) such that the distance \(Q S\) is greatest,
- find an equation of the tangent to \(C\) at \(S\), giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers to be found.