13
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fecb40da-cf47-45e0-801a-1d3d8811b5a0-4_783_766_255_687}
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\caption{Fig. 13}
\end{figure}
Fig. 13 shows the circle with equation \(( x - 4 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 16\).
- Write down the radius of the circle and the coordinates of its centre.
- Find the \(x\)-coordinates of the points where the circle crosses the \(x\)-axis. Give your answers in surd form.
- Show that the point \(\mathrm { A } ( 4 + 2 \sqrt { 2 } , 2 + 2 \sqrt { 2 } )\) lies on the circle and mark point A on the copy of Fig. 13.
Sketch the tangent to the circle at A and the other tangent that is parallel to it.
Find the equations of both these tangents.