Answer
$x=a \cos \dfrac{l}{a}; y= a\sin \dfrac{l}{a}$; $0\leq l \leq 2a\pi$
Work Step by Step
The equation of the circle is $x^2+y^2=a^2$; in parametric form, we have: $x=a \cos \theta; y= a\sin \theta$; $0\leq \theta \leq 2 \pi$
We know that the arc length is given by $l= a \theta$
Or, $\theta=\dfrac{l}{a}$
Thus, the parametric equations become:
$x=a \cos \dfrac{l}{a}; y= a\sin \dfrac{l}{a}$; $0\leq l \leq 2a\pi$
