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

It removes parameter $t$ for a direct $x$ and $y$ relationship.

They are in the form $x = f(t)$ and $y = g(t)$.

Solve one equation for the parameter $t$.

$t = f^{-1}(x)$ if $f^{-1}$ exists.

Substitute $t$ into the other equation $y = g(t)$.

$x = 2t + 3$ and $y = t^2 - 1$.

$y = (x - 3)^2/4 - 1$.

It represents a parabola opening upwards.

Eliminate the parameter using trigonometric identities.

$x^2 + y^2 = 1$, representing a circle.