Implicit and parametric differentiationEdexcel A-Level Maths: Mind map

Exam questions on Implicit and parametric differentiation

1. A curve has equation $x^{2}+y^{2}-4x+6y=12$.
   The point $(5,1)$ lies on the curve. Find an equation of the normal to the curve at $(5,1)$, in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.2 marks
2. A curve $C$ has equation $x^{2}+xy+y^{2}=7$.
   Find the coordinates of the points on $C$ where $\frac{dy}{dx}=0$.2 marks
3. A curve is given by the parametric equations $x=t^{2}+1$, $y=t^{3}-3t$, where $t$ is a real parameter.
   Find $\frac{dy}{dx}$ in terms of $t$, and hence find the gradient of the curve at the point where $t=2$.3 marks