Parametric form

Definition

Parametric form describes a set of equations where the coordinates are expressed as functions of one or more independent parameters. Commonly used to represent curves and surfaces in mathematics, parametric equations provide a convenient way to describe complex geometrical shapes.

5 Must Know Facts For Your Next Test

1. Parametric equations involve a pair (or more) of functions that define the x and y coordinates of points on a curve.
2. The parameter, often denoted by $t$, can represent time or another variable.
3. Converting between parametric and Cartesian forms involves eliminating the parameter.
4. Graphing parametric equations requires plotting points for various values of the parameter.
5. Common examples include representing circles, ellipses, parabolas, and other complex shapes.

Review Questions

• How do you convert a set of parametric equations into Cartesian form?
• What does the parameter $t$ typically represent in parametric equations?
• Give an example of a real-world application where parametric equations are useful.

Related terms

Cartesian Coordinates: A coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the distances from the point to two fixed perpendicular directed lines.

Parameter: An independent variable that expresses coordinates in parametric form; often represented by $t$.

Polar Coordinates: $$(r, \theta)$$: A coordinate system where each point on a plane is determined by an angle and a distance from a reference point.