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