Explanation

(d)
Given foci of ellipse are $(0, - 4)$and (0, 4)
$\therefore$ Focal distance is$\ 2be = 8$
$\ \ be = 4\$ …(i)
Also, since equation of directrices are $\frac{b}{e} = \pm 9$ ...(ii)
From, Eqs. (i) and (ii), we get
$b^{2} = 36\ \Rightarrow \ b = 6\$and$\ e = \frac{2}{3}$
$\because\ a^{2} = b^{2}\left( 1 - e^{2} \right) = 36\ \left( 1 - \frac{4}{9} \right) = 20$
$\therefore\ \frac{x^{2}}{20} + \frac{y^{2}}{36} = 1$
$\Rightarrow \ 9x^{2} + 5y^{2} = 180$