Parametric Equations - Basics (AQA A-Level Mathematics): Flashcards

Curve as $x$ & $y$ functions of third variable (parameter)

$t$

Controls both $x$ and $y$

Remove $t$ to find direct $y = h(x)$ relationship

$\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

$\int y \frac{dx}{dt} dt$

Model motion or curves difficult to describe with $y = f(x)$

Equation written only in terms of $(x, y)$

Third, non-coordinate value defining coordinate variables

Rearrange for $t = ...$, substitute into other equation