CIE A Level Maths: Pure 3复习笔记4.3.1 Parametric Equations - Basics

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 ty 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 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 (ab) and radius r
    • x = rcos θ + a
    • y = rsin θ + b

Worked Example