Parameter

Definition

A parameter is a variable that defines a family of objects or functions, often serving as an independent variable in parametric equations. It allows for the representation of curves and surfaces using coordinates that depend on this variable.

5 Must Know Facts For Your Next Test

1. In parametric equations, parameters are typically denoted by $t$ or other variables like $u$ or $v$.
2. The parameter can represent time in motion problems, allowing you to describe the position of an object at any given moment.
3. Parametric equations often come in pairs or sets, such as $(x(t), y(t))$ for two-dimensional curves.
4. Eliminating the parameter from parametric equations can yield a Cartesian equation relating $x$ and $y$ directly.
5. Parameters simplify the description and calculation of more complex geometric shapes, such as ellipses, circles, and hyperbolas.

Review Questions

• What is a parameter in the context of parametric equations?
• How do parametric equations $(x(t), y(t))$ represent curves in two dimensions?
• Why might one choose to use a parameter to describe geometric shapes?

Related terms

Cartesian Equation: An equation that relates $x$ and $y$ directly without involving a parameter.

Parametric Curve: A curve expressed as a set of parametric equations depending on one or more parameters.

Elimination of Parameter: The process of removing the parameter from parametric equations to obtain a Cartesian equation.