Explanation

(c)
Equation of the ellipse are $\frac{x^{2}}{13^{2}} + \frac{y^{2}}{5^{2}} = 1$ and $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ and their eccentricity are
$e = \sqrt{1 - \frac{25}{169}}$ and $e^{'} = \sqrt{1 - \frac{b^{2}}{a^{2}}}$
According to given condition, $e^{'} = e$
$\Rightarrow \sqrt{1 - \left( \frac{b^{2}}{a^{2}} \right)} = \sqrt{1 - \left( \frac{25}{169} \right)}$
$\Rightarrow \frac{b}{a} = \frac{5}{13}$ $(\because a > 0,\ b > 0)$
$\Rightarrow \frac{a}{b} = \frac{13}{5}$