Figure 2 shows a sketch of part of the curve with parametric equations $$\[ x=2 t^{2}-6 t, \quad y=t^{3}-4 t, \quad t \in \mathbb{R} \]$$ The curve cuts the $$\(x\)$$-axis at the origin and at the points $$\(A\)$$ and $$\(B\)$$, as shown in Figure 2 (a) Find the coordinates of $$\(A\)$$ and show that $$\(B\)$$ has coordinates $$\((20,0)\)$$. (3) (b) Show that the equation of the tangent to the curve at $$\(B\)$$ is $$\[ 7 y+4 x-80=0 \]$$ (5) The tangent to the curve at $$\(B\)$$ cuts the curve again at the point $$\(P\)$$. (c) Find, using algebra, the $$\(x\)$$ coordinate of $$\(P\)$$. (4)

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