9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c08fbab-283e-4c92-89a4-10f68f37e133-14_709_824_118_559}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of part of the curve with parametric equations
$$x = t ^ { 2 } + 2 t , \quad y = t ^ { 3 } - 9 t , \quad t \in \mathbb { R }$$
The curve cuts the \(x\)-axis at the origin and at the points \(A\) and \(B\) as shown in Figure 3 .
- Find the coordinates of point \(A\) and show that point \(B\) has coordinates ( 15,0 ).
- Show that the equation of the tangent to the curve at \(B\) is \(9 x - 4 y - 135 = 0\)
The tangent to the curve at \(B\) cuts the curve again at the point \(X\).
- Find the coordinates of \(X\).
(Solutions based entirely on graphical or numerical methods are not acceptable.)