12.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c6bde466-61ec-437d-a3b4-84511a98d788-40_520_663_255_644}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve \(C\) with parametric equations
$$x = 7 t ^ { 2 } - 5 , \quad y = t \left( 9 - t ^ { 2 } \right) , \quad t \in \mathbb { R }$$
- Find an equation of the tangent to \(C\) at the point where \(t = 1\)
Write your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
The curve \(C\) cuts the \(x\)-axis at the points \(A\) and \(B\), as shown in Figure 3
- Find the \(x\) coordinate of the point \(A\).
- Find the \(x\) coordinate of the point \(B\).
The region \(R\), shown shaded in Figure 3, is enclosed by the loop of the curve \(C\).
- Use integration to find the area of \(R\).