Edexcel A Level Maths: Pure

Revision Notes

9.1.1 Parametric Equations - Basics

A Level Only

What are parametric equations? 

  • Graphs are usually described by a Cartesian equation
    • The equation involves x and y only
  • Equations like this are in the form, or can be rearranged into the form, y = f(x)

 

9.1.1 Notes obj_mot, AS & A Level Maths revision notes

 

  • 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

 

9.1.1 Notes xy_func_t, AS & A Level Maths revision notes

 

  • 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

 

9.1.1 Notes graph_plot, AS & A Level Maths revision notes

 

  • Also see Parametric Equations – Sketching Graphs

 

What is the link between parametric equations and circles? 

9.1.1 Notes par_cicr, AS & A Level Maths revision notes

 

  • 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
A Level Only

Worked Example

9.1.1 Example soltn, AS & A Level Maths revision notes

Author:

After 24 years teaching A Level Further Maths, Maths whizz Simon focused his attention on tutoring. He’s helped thousands of young people make sense of Maths and now he’s helping you too – aren’t you lucky! He’s even worked as an Edexcel examiner, so knows exactly what they’re looking for.
Close

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now