Question

Describe parametric equation of a circle

Answer 1

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

So, here

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

Equation of a circle is given by: $x^2+y^2=r^2(equation(1\left)\right)$

Hence, we have $xandy$ in terms of the given parameter as $x=r\cos \theta andy=r\sin \theta$

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

$$\begin{gathered} \Rightarrow x^2+y^2={\left(r\cos \theta \right)}^2+{\left(r\sin \theta \right)}^2 \\ \Rightarrow x^2+y^2=r^2({\cos }^2\theta +{\sin }^2\theta )=r^2\left[\because {\cos }^2\theta +{\sin }^2\theta =1\right] \\ Hence,x^2+y^2=r^2 \end{gathered}$$