4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{79ac81c3-cd05-4f28-8840-3c8a6960e7b7-10_833_822_127_561}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with parametric equations
$$x = 2 t ^ { 2 } - 6 t , \quad y = t ^ { 3 } - 4 t , \quad t \in \mathbb { R }$$
The curve cuts the \(x\)-axis at the origin and at the points \(A\) and \(B\), as shown in Figure 2.
- Find the coordinates of \(A\) and show that \(B\) has coordinates (20, 0).
- Show that the equation of the tangent to the curve at \(B\) is
$$7 y + 4 x - 80 = 0$$
The tangent to the curve at \(B\) cuts the curve again at the point \(P\).
- Find, using algebra, the \(x\) coordinate of \(P\).