11
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4d8caf0f-7594-42cb-bd40-e6c11e2b6832-3_442_1102_1384_717}
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\caption{Fig. 11}
\end{figure}
A circle has centre \(C ( 1,3 )\) and passes through the point \(A ( 3,7 )\) 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.