Implicit and parametric differentiationEdexcel International A Level Maths: Mind map

Exam questions on Implicit and parametric differentiation

1. A curve $C_1$ has equation $x^3+y^3=9$, and the point $P(1,2)$ lies on $C_1$.
   Find an equation of the tangent to $C_1$ at $P$, in the form $x+by=c$.2 marks
2. A curve $C_2$ has parametric equations $x=t^2+1,\; y=t^3-3t$, where $t$ is a real parameter.
   Find the coordinates of the points on $C_2$ where the tangent is parallel to the $x$-axis.2 marks
3. A curve $C_3$ has parametric equations $x=3\sin t,\; y=2\cos 2t$, for $0\le t<2\pi$.
   Find $\frac{dy}{dx}$ in terms of $t$, giving your answer in its simplest form.3 marks