### Introduction

In this Section we examine yet another way of defining curves - the parametric description. We shall see that this is, in some ways, far more useful than either the Cartesian description or the polar form. Although we shall only study planar curves (curves lying in a plane) the parametric description can be easily generalised to the description of spatial curves which twist and turn in three dimensional space.

#### Prerequisites

• be familiar with Cartesian coordinates
• be familiar with trigonometric and hyperbolic functions and be able to manipulate them
• be able to differentiate simple functions
• be able to locate turning points and distinguish between maxima and minima.

#### Learning Outcomes

• sketch planar curves given in parametric form
• understand how the same curve can be described using different parameterisations
• recognise some conics given in parametric form

3.1 The parabola

3.2 The ellipse