Question

Write the equation of the circle in polar form.

Answer 1

Equation of a circle in polar form.

The equation of a circle centered at the origin with radius $a$ is given by,

$x^2+y^2=a^2$

Substitute $x=r\cos \theta \mathrm{and}y=r\sin \theta$ in the above equation

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

Hence, the equation of the circle is $r=a$.