2.
\begin{figure}[h]
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\caption{Figure 1}
\includegraphics[alt={},max width=\textwidth]{f01026a9-e5fe-4c19-b096-2bb4ad22c389-2_615_833_941_598}
\end{figure}
The circle \(C\), with centre \(( a , b )\) and radius 5 , touches the \(x\)-axis at \(( 4,0 )\), as shown in Fig. 1.
- Write down the value of \(a\) and the value of \(b\).
- Find a cartesian equation of \(C\).
A tangent to the circle, drawn from the point \(P ( 8,17 )\), touches the circle at \(T\).
- Find, to 3 significant figures, the length of \(P T\).