The parametric form of the ellipse is
Step 1: Convert the equation in the standard form
The equation of the given ellipse is,
Step 2: Convert into the parametric form
As we know the parametric equations of an ellipse of the form are,
and
So, the parametric equations of the given ellipse are,
And,
Thus, the required parametric equations of the ellipse are and .
Hence, option (C) is the required option.