Parametric Equations - Eliminating the Parameter (AQA A-Level Mathematics): Flashcards

Removing the parameter $t$ to find a direct relationship between $x$ and $y$

A single Cartesian equation in $x$ and $y$

$x = f(t)$ and $y = g(t)$

Choose the simpler one

Substitute into other equation

$\sin^2 t + \cos^2 t = 1$

Square both equations, then add

$x^2 + y^2 = 1$

Circle with centre $(0,0)$, radius $1$

Move between parametric & Cartesian forms