14.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{08b1be3e-2d9a-4832-b230-d5519540f494-48_771_812_237_575}
\captionsetup{labelformat=empty}
\caption{Figure 5}
\end{figure}
Figure 5 shows a sketch of the circle \(C _ { 1 }\)
The points \(A ( 1,4 )\) and \(B ( 7,8 )\) lie on \(C _ { 1 }\)
Given that \(A B\) is a diameter of the circle \(C _ { 1 }\)
- find the coordinates for the centre of \(C _ { 1 }\)
- find the exact radius of \(C _ { 1 }\) simplifying your answer.
Two distinct circles \(C _ { 2 }\) and \(C _ { 3 }\) each have centre \(( 0,0 )\).
Given that each of these circles touch circle \(C _ { 1 }\) - find the equation of circle \(C _ { 2 }\) and the equation of circle \(C _ { 3 }\)