10.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{937246f9-2b6a-48df-b919-c6db3d6f863b-28_643_1171_260_518}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve \(C\) with equation
$$y = \frac { 1 } { 2 } x + \frac { 27 } { x } - 12 , \quad x > 0$$
The point \(A\) lies on \(C\) and has coordinates \(\left( 3 , - \frac { 3 } { 2 } \right)\).
- Show that the equation of the normal to \(C\) at \(A\) can be written as \(10 y = 4 x - 27\)
The normal to \(C\) at \(A\) meets \(C\) again at the point \(B\), as shown in Figure 3.
- Use algebra to find the coordinates of \(B\).