Home >> PURE MATHS, Coordinate Geometry, parametric equations

Introduction

There is another way of writing y as a function of x and that is to use two separate equations.

One equation has x as a function of t (or θ) eg x = 2t .

The other equation has y as function of t (or θ) eg y = t² .

The variables t, θ are called parameters and the two equalities parametric equations.

Common questions on this topic are the plotting of parametric equations and their conversion to a single Cartesian equation.

Example #1

Plot the graph of the curve given parametrically by the equations:

x = 2cosθ         y = 2sinθ

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Example #2

What is the Cartesian equation given parametrically by:

x = t²+3          y = t³ + 3t

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Example #3

What is the Cartesian equation given parametrically by:

x = 2sinθ          y = 2sin2θ

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