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 x2 + y2 = r2.
Let us proceed step by step.
We will use the independent variable r and θ as the parameter.
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 analysing the figure shown below: