10.1 Curves Defined by Parametric Equations Parametric Equations & Parametric Curves 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 . Collections: Mathematics