 
Summary: 10.1 Curves Defined by Parametric Equations
Parametric Equations & Parametric Curves
· Parametric Equations: If x and are both functions of a third variable t ,
that is,
y
( ) ( ),x f t y g t= =
Then these equations are called parametric equations and the third variable
t is called parameter.
· Each value of t determines a point ( , )x y , which we can plot in a
coordinate plane.
· As t varies, the point ( , ) ( ( ), ( ))x y f t g t= varies and traces out a curve,
called parametric curve.
· The curve with parametric equations
( ) ( ),x f t y g t a t= = b
has initial point ( ( ), ( ))f a g a and the terminal point ( ( ), ( ))f b g b .
· A curve may have more than one set of parametric equations, for example,
cos , sin and sin2 , cos2x t y t x t y t= = = =
represent circle with center at origin and radius one.
· The graph of the parametric curve can be determined by plotting ( , )x y
corresponding to parameter t .
