Explanation

(a)
Given , $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$
$\therefore e = \sqrt{1 - \frac{9}{16}} = \frac{\sqrt{7}}{4}$
$\therefore Coodinates\ of\ foci\ are\ \left( \pm \sqrt{7,}0 \right)$
Since, centre of circle is (0, 3) and passing through foci $( \pm 7,\ 0)$
$\therefore$ Radius of circle$= \sqrt{\left( 0 \pm \sqrt{7} \right)^{2} + (3 - 0)^{2}}$
$= \sqrt{7 + 9} = 4$