Parametric Equations

Definition

Parametric equations are a set of equations that express the coordinates of points on a curve or surface in terms of one or more parameters. They allow us to represent complex shapes and motions by breaking them down into simpler components.

Related terms

Parametric Functions:

These are functions defined by parametric equations, where each coordinate is expressed as a function of the parameter(s). For example, x = f(t) and y = g(t) would define a parametric function.

x = f(t): This is one part of a parametric equation that represents the x-coordinate in terms of the parameter t. It tells us how the x-value changes as t varies.

y = g(t): This is another part of a parametric equation that represents the y-coordinate in terms of the parameter t. It tells us how the y-value changes as t varies.