Instead of one equation relating say, x and y, we have two equations, one relating x with the parameter, and one relating y with the parameter.
Sometimes x and y are given as functions of a single variable, e.g., are two functions and t is a variable. In such a case x and y are called parametric functions or parametric equations and t is called the parameter.
To find in case of parametric function , we first obtain the relationship between x and y by eliminating the parameter t and then we differentiate at with respect to x . But every time it is not convenient to eliminate the parameter . Therefore acn also be obtained by following formula
To prove it , let be the changes in x and y respectively corresponding to a small change
Differentiating w.r.t. θ , we get