A-level · Coordinate geometry

Parametric curves and trig identitiesExam-style questions

Converting trigonometric parametric equations to Cartesian form using identities — sin²+cos²≡1 for circles and ellipses, sec²−tan²≡1, and the double-angle formulae — and recognising the curve that results.

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16 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
The diagram shows a curve $C$ with parametric equations $x = 5\cos t,\ y = 2\sin t$ , $0 \le t < 2\pi$ .Find a Cartesian equation of $C$ .
Level 3 · 2 marksTry it
2
A curve has parametric equations $x = 2 + 3\cos t,\ y = 1 + 3\sin t$ . Find a Cartesian equation of the curve and state its centre and radius.
Level 3 · 2 marksTry it
3
A curve has parametric equations $x = 4\cos t, \; y = 3\sin t$ , $\; 0 \leqslant t < 2\pi$ .
(a) Find a Cartesian equation of the curve. (3 marks)
(b) State the range of possible values of $x$ . (1 mark)
Level 3 · 4 marksTry it
4
A curve has parametric equations $x = 1 + 2\cos t, \; y = -3 + 2\sin t$ , $\; 0 \leqslant t < 2\pi$ .

Find a Cartesian equation of the curve, and state what the curve is. (4 marks)
Level 3 · 4 marksTry it