Basics of Parametric Equations (Cambridge (CIE) A Level Maths): Revision Note

Parametric Equations - Basics

What are parametric equations? 

• Graphs are usually described by a Cartesian equation

  • The equation involves x and y only

• Equations like this can sometimes be rearranged into the form, y = f(x)

• In parametric equations both x and y are dependent on a third variable

  • This is called a parameter

  • t and θ are often used as parameters

• A common example …

  • x is the horizontal position of an object

  • y is the vertical position of an object

  • and the position of the object is dependent on time t

• x is a function of t, y is a function of t

  • x = f(t)

  • y = g(t)

What do I do with parametric equations?

• It is still possible to plot a graph of y against x from their parametric equations

• Also see Parametric Equations – Sketching Graphs

What is the link between parametric equations and circles? 

• For a circle, centre (0, 0) and radius r

  • x = rcos θ

  • y = rsin θ

  • (Note that r is constant, this is not two parameters)

• For a circle, centre (a, b) and radius r

  • x = rcos θ + a

  • y = rsin θ + b