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.,Â 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 findÂ in case of parametric function , we first obtain the relationshipÂ between x and yÂ 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 . ThereforeÂ Â acn also be obtained by following formula

To prove it , let Â be the changes in x and y respectively corresponding to a small change

### Example

**Solution:**

Differentiating w.r.t.Â Î¸ , we get