A-level · Coordinate geometry

Intersections of parametric curvesExam-style questions

Finding where a parametric curve meets the coordinate axes, a given line, or another curve — by solving for the parameter — and using a repeated root to detect a tangent.

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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 $x = 2t,\ y = t^2 - 2t - 3$ . Find the coordinates of the points where the curve crosses the $x$ -axis.
Level 3 · 3 marksTry it
2
A curve has parametric equations $x = t^2,\ y = 2t$ . Find the coordinates of the points where the curve meets the line $y = x - 3$ .
Level 3 · 3 marksTry it
3
A curve has parametric equations $x = t + 1,\ y = t^2$ . Find the coordinates of the points where the curve meets the line $y = x + 1$ .
Level 3 · 3 marksTry it
4
The line $y = 3x - 4$ meets the curve with parametric equations $x = 2t,\ y = t^2 + 1$ . Find the coordinates of the two points of intersection.
Level 3 · 3 marksTry it
5
A curve has parametric equations $x = t^2 - 1,\ y = 2t$ .
(a) Find the coordinates of the point where the curve meets the $x$ -axis.
(b) Find the coordinates of the points where the curve meets the $y$ -axis.
Level 3 · 4 marksTry it

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