Explanation

(d)
Given that, foci are $(3,\ 0)$ and $( - 1,\ 0)$ and $e = \frac{2}{3}$
$\therefore\ 2ae = 4 \Rightarrow \ a = 3$
Also, $e^{2} = 1 - \frac{b^{2}}{a^{2}}$
$\Rightarrow \ \frac{4}{9} = 1 - \frac{b^{2}}{9}$
$\Rightarrow \ b = \sqrt{5}$
Since, centre of the ellipse is the mid point of the line joining the two foci, therefore the coordinates of the centre are (1, 0)
$\therefore$ Equation of ellipse is
$\frac{(x - 1)^{2}}{9} + \frac{(y - 0)^{2}}{5} = 1$
Hence, the parametric coordinates are $(1 + 3\cos{\theta,\sqrt{5}}\sin\theta)$