3
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{50cfc73d-850e-4a9b-b088-cc9741b66ffb-2_445_617_1008_741}
\captionsetup{labelformat=empty}
\caption{Fig. 11}
\end{figure}
Not to scale
A circle has centre \(\mathrm { C } ( 1,3 )\) and passes through the point \(\mathrm { A } ( 3,7 )\) as shown in Fig. 11.
- Show that the equation of the tangent at A is \(x + 2 y = 17\).
- The line with equation \(y = 2 x - 9\) intersects this tangent at the point T .
Find the coordinates of T .
- The equation of the circle is \(( x - 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 20\).
Show that the line with equation \(y = 2 x - 9\) is a tangent to the circle. Give the coordinates of the point where this tangent touches the circle.