AQA A Level Maths: Pure复习笔记9.1.1 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 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

Worked Example