For the curve, the parametric equations are $x = t^3 + 6t + 1$ and $y = t^4 - 2t^3 + 4t^2 - 12t + 5$.
(i)[5]
Find $\frac{dy}{dx}$ and use division to demonstrate that $\frac{dy}{dx}$ may be expressed as $at + b$, where $a$ and $b$ are constants to be determined.
(ii)[3]
The line $x - 2y + 9 = 0$ acts as the normal to the curve at point $P$. Determine the coordinates of $P$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $x$ and $y$, then form $\dfrac{dy}{dx}$” …