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Parametric equations define x and y separately in terms of a parameter t. This topic covers plotting parametric curves and converting to Cartesian form by eliminating the parameter. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Both coordinates are given in terms of a parameter. To convert to Cartesian, make the parameter the subject of one equation and substitute into the other, or use a trig identity when the parameter is an angle. State any restriction on x or y that the parameter imposes.
Before you start
Get coordinates and trigonometric identities straight before you begin. It carries straight through to parametric differentiation and areas. You meet it in Pure 4.
What you learn
To find the ordinary Cartesian equation you must eliminate t — sometimes by substitution, sometimes with a trig identity. and problem solving. A parametric curve gives x and y separately, each in terms of t. When x and y both involve trig functions, you cannot rearrange for t — you must eliminate it with an identity. If one equation contains 2t (or t+α), expand it first with a double-angle or addition formula — then the elimination becomes routine. The course works through eliminating t by substitution, eliminating t with a trig identity, double and compound angles, domain and range — which part of the curve? Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Parametric Equations is part of the Coordinate Geometry strand of our free A-level maths courses, studied in the AS year. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Students often pair it with Straight Lines, Circles — Equation & Properties, Circles — Tangents & Chords and Distance & Midpoint. You can drill this strand further on the Coordinate Geometry revision engine, with your accuracy saved to your skill tree.
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