Explanation

(b)
Since, the coordinates of foci of hyperbola are $( - 5,3)$ and $(7,\ 3)$
$\therefore\ 2ae = 7 - ( - 5) = 12$
$\Rightarrow \ a = \frac{12 \times 2}{3 \times 2} = 4\ \ \ \ \lbrack\because e = 3/2\rbrack$
$e = \sqrt{1 + \frac{b^{2}}{a^{2}}\ } \Rightarrow \ \frac{9}{4} - 1 = \frac{b^{2}}{16}$
$\Rightarrow \ b^{2} = 20\$
Hence, length of latusrectum $= \ \frac{2b^{2}}{a} = \frac{2 \times 20}{4} = 10$