Drop perpendicular PA on x- axis, with point A on x-axis.

$therefore $ in triangle $\Delta OPA$

$ OP = a $ units, and $OA = x$ also $AP = y$

$\therefore Cos\theta = \cfrac{OA}{OP}=\cfrac{x}{a}\,—-(1)$

and $Sin\theta = \cfrac{AP}{OP}=\cfrac{y}{a}\,—-(2)$

Hence from (1) and (2) we get,

$x\,=\,aCos\theta$ and $y=\,=\,aSin\theta$

** Hence parametric equation of circle with center as origin and radius as ‘a’ units is $x\,=\,aCos\theta$ and $y=\,=\,aSin\theta$ where $\theta$ is a parameter and $\theta \in [0,2\pi)$**