# Describe the parametric equation of a circle.

In the parametric equation, we use an independent variable which is also known as a parameter.

## Answer: x = r cos θ and y = r sin θ represent the parametric equations of the circle x^{2} + y^{2} = r^{2}.

Let us proceed step by step.

**Explanation:**

We will use the independent variable r and θ as the parameter.

Equation of a circle is given by: x^{2} + y^{2} = r^{2}---------(1)

Hence, we have x and y in terms of the given parameter as x = r cos θ and y = r sin θ

Let us substitute the given parameter in equation 1, we get

(r cos θ)^{2} + (r sin θ)^{2} = r^{2}

r^{2} ( cos^{2}θ + sin^{2}θ ) = r^{2}

since cos^{2}θ + sin^{2} θ = 1 [ from trigonometric identites ]

we can understand better by analysing the figure shown below: