Coordinate geometry: parametric equations

Sample questions

Original practice questions written in the style of the exam.

1. Question 15 marks

   The curve $C$ has parametric equations

   $x = 1 + 2t, \quad y = \frac{4}{t}, \quad t \neq 0$

   (a) Find a Cartesian equation of $C$ in the form $y = f(x)$.

   (b) Find the coordinates of the points where $C$ meets the line $y = x + 1$.

   Mark scheme

   • M1 Writes $t = \dfrac{x - 1}{2}$ and substitutes into $y$ (1)
   • A1 $y={\displaystyle }$ (1)