Explanation

(b)
The vertices and foci of an ellipse are $( \pm 5,\ 0)$ and $( \pm 4,\ 0)$ respectively
$\therefore a = 5$ and $ae = 4$
$\Rightarrow \ \ e = \frac{4}{5}$
$\because\ e = \sqrt{1 - \frac{b^{2}}{a^{2}}}$
$\Rightarrow \ \ \frac{16}{25} = 1 - \frac{b^{2}}{25}$
$\Rightarrow \ \ b^{2} = 9\$
Hence, equation of an ellipse is
$\frac{x^{2}}{25} + \frac{y^{2}}{9} = 1\ \Rightarrow \ 9x^{2} + 25y^{2} = 225$