A-level · Coordinate geometry

Parametric curvesExam-style questions

Defining a curve by parametric equations x = f(t), y = g(t), finding the coordinates of points on the curve, finding the parameter value at a given point, and reading off the range of x- and y-values from the domain of t.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3

1
A curve has parametric equations $x = 2t,\ y = t^2 - 4t$ for $-1 \le t \le 5$ . Find the range of values of $x$ and the range of values of $y$ .
Level 3 · 3 marksTry it
2
A curve has parametric equations $x = t + 1,\ y = \dfrac{4}{t}$ , $t \ne 0$ .
(a) Find the coordinates of the point where $t = 2$ .
(b) Find the value of $t$ for which $x = 5$ , and the corresponding $y$ .
(c) Explain why the curve never meets the $x$ -axis.
Level 3 · 4 marksTry it
3
A curve $C$ has parametric equations $x = t^2,\ y = t^3$ , $t \in \mathbb{R}$ .
(a) Show that both $(4, 8)$ and $(4, -8)$ lie on $C$ , stating the value of $t$ at each.
(b) Explain why no point of $C$ has a negative $x$ -coordinate.
Level 3 · 3 marksTry it
4
A curve $C$ has parametric equations $x = t^2 - 3,\ y = t^3 - 3t$ .
(a) Find the coordinates of the points on $C$ where $t = -2, -1, 0, 1$ and $2$ .
(b) Show that $C$ is symmetric about the $x$ -axis.
Level 3 · 4 marksTry it
5
A curve has parametric equations $x = t - \dfrac{3}{t},\ y = t + \dfrac{3}{t}$ , for $t > 0$ . Find the value of $t$ for which $x = 2$ , and the coordinates of the corresponding point.
Level 3 · 3 marksTry it

7 more questions on parametric curves

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

Start free