Explanation

(a)
Distance between two foci, $2ae = 7 + 1 = 8\$
$\therefore\ \ ae = 4 \Rightarrow \ a = 8\ \ \left\lbrack \therefore e = \frac{1}{2},\ given \right\rbrack$
$\because b^{2} = a^{2}\left( 1 - e^{2} \right) = 64\ \left( 1 - \frac{1}{4} \right)$
$\Rightarrow \ \ b = 4\sqrt{3}$
Since, the centre of the ellipse is the mid point of the line joining two foci, therefore the coordinates of the centre the (3, 0)
$\therefore I$ts equation is$\$
$\frac{(x - 3)^{2}}{8^{2}} + \frac{(y - 0)^{2}}{\left( 4\sqrt{3} \right)^{2}} = 1$ …(i)
Hence, the parametric coordinates of a point on Eq.(i) are $(3 + 8\cos{\theta,\ 4\sqrt{3}}\sin{\theta\ )}$