Explanation

(c)
Given equation can be rewritten as
$\frac{(x - 1)^{2}}{9} - \frac{y^{2}}{3} = 1$ …(i)
Then, equation of its conjugate hyperbola will be
$\frac{y^{2}}{3} - \frac{(x - 1)^{2}}{9} = 1$ …(ii)
Here, $a^{2} = 9,\ \ b^{2} = 3$
$\therefore\ \ \ a^{2} = b^{2}\left( e^{2} - 1 \right)\ \Rightarrow \ \ 9 = 3\left( e^{2} - 1 \right)$
$\Rightarrow \ e^{2} - 1 = 3\ \Rightarrow \ \ e = 2$