Explanation

(d)
Let $e$ and $e’$ be the eccentricities of the ellipse and hyperbola
$\therefore e = \sqrt{\frac{{a^{2} - \ b}^{2}}{a^{2}}} = \ \sqrt{\frac{25 - 16}{25}} = \frac{3}{5}$
and$\ \ e’ = \sqrt{\frac{{a^{2} + b}^{2}}{a^{2}}} = \sqrt{\frac{25 + 16}{25}\ } = \frac{\sqrt{41}}{5}$
Centre of ellipse is (0, 0) and centre of hyperbola is (0, 0)
Foci of ellipse are $( \pm ae,0)$ or $( \pm 3,0)$ foci of hyperbola are ($\pm ae^{'},0)$ or $\left( \pm \sqrt{41},\ 0 \right)$
Directrices of ellipse are $x = \pm \frac{a}{e} \Rightarrow x = \pm \frac{25}{3}$
Directrices of hyperbola are $x = \pm \frac{a}{e}$
$\Rightarrow \ x = \pm \frac{25}{\sqrt{41}}$
Vertices of ellipse are $( \pm a,0)$ or $( \pm 5,0)$
Vertices of hyperbola are $( \pm a,0)$ or $( \pm 5,0)$
From the above discussions, their are common in centre and vertices.