Parametric Equations - Basics (CIE AS Maths: Pure 2)

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