2.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{2bacec90-3b67-4307-9608-246ecdb6b5e2-06_695_700_251_683}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of part of the curve \(C\) with equation
$$2 ^ { x } - 4 x y + y ^ { 2 } = 13 \quad y \geqslant 0$$
The point \(P\) lies on \(C\) and has \(x\) coordinate 2
- Find the \(y\) coordinate of \(P\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(x\) and \(y\).
The tangent to \(C\) at \(P\) crosses the \(x\)-axis at the point \(Q\).
- Find the \(x\) coordinate of \(Q\), giving your answer in the form \(\frac { a \ln 2 + b } { c \ln 2 + d }\) where \(a , b , c\) and \(d\) are integers to be found.