Q.Find the parametric representation of the circle $3x^2+3y^2-4x+6y-4=0$.

Instead of describing a circle by an equation relating $x$ and $y$, the parametric form describes every point on it using a single variable $\theta$ — the angle that the radius to that point makes with the positive $X$-axis. For the standard circle $x^2+y^2=r^2$, dropping a perpendicular from a point $P(x,y)$ on the circle to the $X$-axis creates a right triangle giving $\cos\theta=x/r$ and $\sin\theta=y/r$, i.e.

$x=r\cos\theta, \qquad y=r\sin\theta$ …