- In this question you must show all stages of your working.
\section*{Solutions based entirely on calculator technology are not acceptable.}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f6af51c1-5f85-4952-b3c4-9dca42b2a309-26_761_940_411_566}
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\caption{Figure 3}
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Figure 3 shows
- the curve \(C\) with equation \(y = x ^ { 2 } - 4 x + 5\)
- the line \(l\) with equation \(y = 2\)
The curve \(C\) intersects the \(y\)-axis at the point \(D\).
- Write down the coordinates of \(D\).
The curve \(C\) intersects the line \(l\) at the points \(E\) and \(F\), as shown in Figure 3.
- Find the \(x\) coordinate of \(E\) and the \(x\) coordinate of \(F\).
Shown shaded in Figure 3 is
- the region \(R _ { 1 }\) which is bounded by \(C , l\) and the \(y\)-axis
- the region \(R _ { 2 }\) which is bounded by \(C\) and the line segments \(E F\) and \(D F\)
Given that \(\frac { \text { area of } R _ { 1 } } { \text { area of } R _ { 2 } } = k\), where \(k\) is a constant, - use algebraic integration to find the exact value of \(k\), giving your answer as a simplified fraction.