Describe the parametric equation of a circle.

Solution:

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

Let us proceed step by step.

We will use the independent variables r and θ as the parameters.

Equation of a circle is given by: x² + y² = r²---------(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 = r²

r² ( cos²θ + sin²θ ) = r²

since cos²θ + sin² θ = 1 [ from trigonometric identites ]

we can understand better by analyzing the figure shown below:

Therefore, x = r cos θ and y = r sin θ represent the parametric equations of the circle x² + y² = r².

Describe the parametric equation of a circle.

Summary:

 x = r cos θ and y = r sin θ represent the parametric equations of the circle x² + y² = r².