Explanation

(b)
Let the equation of hyperbola is
$\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ …(i)
It passes through the point (3, 0) and ($3,\ \sqrt{2},2).$
$\therefore\ \frac{9}{a^{2}} = 1\ \Rightarrow a^{2} = 9$
And $\frac{18}{a^{2}} - \frac{4}{b^{2}} = 1\ \Rightarrow \frac{4}{b^{2}} = \frac{18}{9} - 1$
$\Rightarrow \ \frac{4}{b^{2}} = 1\ \Rightarrow b^{2} = 4$
$\therefore\$ Eccentricity of hyperbola,
$e = \sqrt{1 + \frac{b^{2}}{a^{2}}} = \sqrt{1 + \frac{4}{9}} = \frac{\sqrt{13}}{3}$