length of circumference of a circle

Question

Find the length of the circumference of a circle, whose equation is $r=2acos\theta$. I have tried differentiating with respect to $\theta$. I don't know what to do next. I seek a formula for solving this problem.

Answer 1

Multiply by $r$ and change to Cartesian coordinates to get $$(x-a)^2+y^2=a^2$$ which is a circle.

The radius is $a$ so the circumference is $$2\pi a$$

Answer 2

HINT

Recall that by polar coordinates

• $r=x^2+y^2$
• $x=r\cos \phi$
• $y=r\sin \phi$