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How do I find the cartesian equation for a curve written in parametric form?

Reminder - a cartesian equation is written in terms of x and y (e.g. y = 2x + 3) while parametric equations are written with x and y separately in terms of t.

Example: Find the cartesian equation of the curve given by these parametric equations:

x = 2t + 1, y = 1/t (where t is not equal to zero)

First make t the subject in one of the equations.

x = 2t (then divide both sides by 2)

x/2 = t

Now substitute your result for t into the second equation.

y = 1/t (then substitute in t = x/2)

y = 1/(x/2) (then simplify)

y = 2/x

This is now in cartesian form.
 

Alexis O. GCSE Maths tutor, A Level Maths tutor

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