Eliminating the Parameter of Parametric Equations (Cambridge (CIE) A Level Maths): Revision Note

Parametric Equations - Eliminating the Parameter

What does eliminating the parameter mean? 

• In parametric equations, x = f(t) and y = g(t)

• There is still a connection directly linking x and y

  • This will be the Cartesian equation of the graph

How do I find the Cartesian equation from parametric equations? 

• STEP 1: Rearrange one of the equations to make t the subject

  • Either t = p(x) or t = q(y)

• STEP 2: Substitute into the other equation

• STEP 3 Rearrange into the desired (Cartesian) form

How do I eliminate t when trig is involved?

• STEP 1  Rearrange both equations into the forms “cos t = …” and “sin t = …”

• STEP 2  Square BOTH sides of BOTH equations

• STEP 3  Add the equations together

• STEP 4  The trig identity “sin² x + cos² x ≡ 1” eliminates t

• STEP 5  Rearrange into desired (Cartesian) form

  • This technique is seen in Trigonometric Identities