Basics of Parametric Equations (Cambridge (CIE) AS Maths) : Revision Note

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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)

 

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

  • 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

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

Worked Example

9.1.1 Example soltn, AS & A Level Maths revision notes
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