Answer
\[
\frac{1}{a}
\]
Work Step by Step
We find:
\[
\kappa=\frac{\left|2\left(\frac{d r}{d \theta}\right)^{2}-r \frac{d^{2} r}{d \theta^{2}}+r^{2}\right|}{\left[r^{2}+\left(\frac{d r}{d \theta}\right)^{2}\right]^{3 / 2}}
\]
Let $a=r$ be the circle.
And then
$0=d r / d \theta,$ and
\[
\frac{1}{a}=\frac{1}{r}=\frac{\left|r^{2}\right|}{r^{3}}=\kappa(\theta)
\]
