**Topic: **Parametric Equations

**When:** Friday, April 23 @ 11:00am

**Who:** Professor Dan Balaguy

**Where: **Canvas (https://sierra.instructure.com/courses/347458)

A **parametric equation** defines a group of quantities as functions of one or more independent variables called parameters.^{[1]} Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface, in which case the equations are collectively called a **parametric representation** or **parameterization** (alternatively spelled as **parametrisation**) of the object.^{[1]}^{[2]}^{[3]}

For example, the equations

form a parametric representation of the unit circle, where *t* is the parameter: A point (*x*, *y*) is on the unit circle if and only if there is a value of *t* such that these two equations generate that point. Sometimes the parametric equations for the individual scalar output variables are combined into a single parametric equation in vectors: