Parametric equation
![One example of a sketch defined by parametric equations is
the butterfly curve.](/Images/godic/202502/01/Butterfly_trans01.svg3002.png")
![](/Images/godic/202502/01/Lissajous_curve_3by2.svg3002.png")
![](/Images/godic/202502/01/2-circles_hypotrochoid3002.gif")
![](/Images/godic/202502/01/HypotrochoidOutThreeFifths3002.gif")
In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter. For example,
are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a parametric representation of the curve.