A parametric function describes a set of related quantities as functions of one or more independent variables, called parameters. Instead of expressing one variable directly in terms of another, like y as a function of x, a parametric function defines both x and y separately in terms of a third variable, often denoted t. As t varies over a given range, it traces out a curve or path in the plane (or space) by producing corresponding pairs (x(t), y(t)). This approach is especially useful for model