A-level · Coordinate geometry

Converting to Cartesian formExam-style questions

Eliminating the parameter to find the Cartesian equation of a parametric curve, by substitution or rearrangement, and carrying the domain restriction from the parameter through to the Cartesian equation.

Start practising Read the lesson

23 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A curve has parametric equations $x = t + 1,\ y = t^2$ . Find a Cartesian equation of the curve.
Level 2 · 2 marksTry it
2
A curve has parametric equations $x = 2t,\ y = t^2 - 3$ . Find a Cartesian equation of the curve.
Level 2 · 2 marksTry it
3
A curve has parametric equations $x = t - 3, \; y = 2t + 1$ .

Find a Cartesian equation of the curve, and state what kind of curve it is. (3 marks)
Level 2 · 3 marksTry it
4
A curve has parametric equations $x = 3t, \; y = t^{2}$ .

Find a Cartesian equation of the curve. (3 marks)
Level 2 · 3 marksTry it
5
A curve $C$ has parametric equations

$x = 2\cos t$ , $\quad y = \cos 2t$ , $\quad 0 \le t \le \pi$ .
(a) Show that $\dfrac{\mathrm{d}y}{\mathrm{d}x} = 2\cos t$ . (3 marks)
(b) Find the Cartesian equation of $C$ , stating the range of values of $x$ for which the curve is defined. (3 marks)
(c) Verify that differentiating your Cartesian equation gives a result consistent with part (a). (1 mark)
Level 3 · 7 marksTry it

18 more questions on converting to cartesian form

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free