Introduction to Parametric Equations

This lesson introduces parametric equations, a powerful way to describe curves in the coordinate plane. Instead of expressing y directly in terms of x, we express both x and y in terms of a third variable called a parameter (usually t or θ). Parametric equations are an important topic in A-Level Mathematics, appearing in pure mathematics, mechanics (where time is a natural parameter), and further mathematics.

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What Are Parametric Equations?

A curve is defined parametrically when both coordinates are given as functions of a parameter:

x = f(t),  y = g(t)

As the parameter t varies, the point (x, y) traces out the curve. Each value of t gives a specific point on the curve.

Example 1: The parametric equations x = 2t, y = t² define a curve. Find some points.