Explanation

(c)
Given equation can be written as
$24\left( x^{2} - 5x + \frac{25}{4} \right) + 9\left( y^{2} - 10y + 25 \right)$
$+ 225 - 150 - 225 = 0$
$\Rightarrow \ \ \frac{\left( x - \frac{5}{2} \right)^{2}}{\frac{150}{24}} + \frac{(y - 5)^{2}}{\frac{150}{9}} = 1$
$\therefore\ e = \sqrt{1 - \frac{a^{2}}{b^{2}}} = \sqrt{1 - \frac{9}{24}} = \sqrt{\frac{15}{24}}$