Implicit and parametric differentiationAQA A-Level Maths: Mind map

Exam questions on Implicit and parametric differentiation

1. A curve has equation $x^2+y^2-6x+4y=12$.
   Find the coordinates of the points on the curve where the tangent is parallel to the $y$-axis.2 marks
2. A curve has equation $xy^2+x^2=6$ and passes through the point $(2,1)$.
   Find the equation of the tangent to the curve at $(2,1)$, in the form $ax+by=c$ with integer coefficients.2 marks
3. A curve is defined by the parametric equations $x=t^2+2t$ and $y=t^3-3t$, where $t$ is a real parameter.
   Show that $\frac{dy}{dx}=\frac{3(t-1)}{2}$ for $t\ne-1$.3 marks