Parametric Curves:

In parametric form each of coordinate of a point on a curve is represented as a function of a single parameter. The position vector of any point on the curve is fixed by the value of the parameter. For a two-dimensional curve along with t like the parameter, the cartesian coordinates of a point on the curve are following:

                                   x = x (t)

                                    y = y (t)

The position vector of any point on the curve is then

                                                 P (t) = [x (t) y (t)]*

The nonparametric form is attained from the parametric form by eliminating the parameter to obtain a single equation in terms of x and y.

The parametric form is proper for representing closed and multiple valued curves. The derivative or tangent vector on a parametric curve is given by:

P′ (t) = [x′ (t) y′ (t)]

where the ′ indicate differentiation with respect to the parameter. The slope of the curve,

dy/dx, is

dy /dx =  (dy /dt)  / (dx/dt )= y′ (t ) / x′ (t)

Note down that when x' (t) = 0, the slope is infinite. Therefore an infinite slope is specified by letting one component of the tangent vector to be zero. Therefore, computational difficulties are ignored by using the parametric derivative.