The ellipse& (x2)/(25) + (y2)/(16) = 1 and the hyperbola~ (x2)/(25)...

For ellipse& $\dfrac{x2}{25} + \dfrac{y2}{16} = 1, a = 5$~and~$b = 4$

Center $= \left(0, 0\right)$, vertices \left(\pm5, 0\right)$<br />~For hyperbola~\dfrac{x2}{25} - \dfrac{y2}{16} =$1, a = 5$and~$b = 4$</p><p>Center \left(0, 0\right)$, vertices \left(\pm5, 0\right)

For ellipse~$a^{2}e^{2} = a^{2} - b^{2} = 25 - 16 = 9$

For hyperbola~

$a^{2}e^{2} = a^{2} + b^{2} = 25 + 16 = 41$.

$∴$& Only center and vertices are common.