Explanation

(c)
Given equation can be rewritten as
$\Rightarrow 4\left( x^{2} - 6x + 9 \right) + 16\left( y^{2} - 2y + 1 \right) - 36 - 6 = 1$
$\Rightarrow \ \frac{(x - 3)^{2}}{\frac{53}{4}} + \frac{(y - 1)^{2}}{\frac{53}{16}} = 1$
Here , $a^{2}\ = \frac{53}{4}\ \$and$\$ $b^{2} = \frac{53}{16}$
$\therefore$ Eccentricity of ellipse is $e = \frac{\sqrt{a^{2} - b^{2}}}{a^{2}}$
$\Rightarrow \ e = \frac{\sqrt{\frac{53}{4} - \frac{53}{16}}}{\frac{53}{4}}$
$\Rightarrow \ e = \frac{\sqrt{3}}{2}$