Explanation

(b)
Given equation of hyperbola can be rewritten as
$x(y - 3) - 3(y - 3) = 2\ \Rightarrow (x - 3)(y - 3) = 2$
Let $x - 3 = X$ and $y - 3 = Y$
Equation of hyperbola is of the form $XY = 2$ (rectangular hyperbola). In rectangular hyperbola $a = b$, so length of latusrectum $= \frac{2b^{2}}{a} = 2a$ (distance between vertices)
and $xy = c^{2}\ \Rightarrow 2 = \frac{a^{2}}{2} \Rightarrow a = 2$
$\therefore\ \$Length of latusrectum is $2a = 4$