The curve $C$ is defined parametrically by

1. Find the gradient of the curve at the point where $y=-\frac{\pi }{4}$.

2. Prove that $C$ is a parabola, giving its equation in Cartesian form.

For part (b), remember that

Use the above hint with the fact that $\sin (t)=x-1$ to get the Cartesian equation.

If the Cartesian equation of the parabola is

give the value of $abc$.