## Summary of Parametric Equations

### Essential Concepts

• Parametric equations provide a convenient way to describe a curve. A parameter can represent time or some other meaningful quantity.
• It is often possible to eliminate the parameter in a parameterized curve to obtain a function or relation describing that curve.
• There is always more than one way to parameterize a curve.
• Parametric equations can describe complicated curves that are difficult or perhaps impossible to describe using rectangular coordinates.

## Glossary

cusp
a pointed end or part where two curves meet
cycloid
the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line without slippage
orientation
the direction that a point moves on a graph as the parameter increases
parameter
an independent variable that both x and y depend on in a parametric curve; usually represented by the variable t
parametric curve
the graph of the parametric equations $x\left(t\right)$ and $y\left(t\right)$ over an interval $a\le t\le b$ combined with the equations
parametric equations
the equations $x=x\left(t\right)$ and $y=y\left(t\right)$ that define a parametric curve
parameterization of a curve
rewriting the equation of a curve defined by a function $y=f\left(x\right)$ as parametric equations