Explanation

(b)
The centers and radii of given circles are $C_{1}(4,\ - 1),\ C_{2}(1,\ 8)$
and $r_{1} = \sqrt{16 + 1 + 0} = \sqrt{17}$
$r_{2} = \sqrt{1 + 64 - 25} = \sqrt{40}$
Now, $C_{1}C_{2} = \sqrt{(1 - 4)^{2} + (8 + 1)^{2}} = \sqrt{90}$
and $r_{1} + r_{2} = \sqrt{17} + \sqrt{40}$
$\therefore\ \ \ \ C_{1}C_{2} < r_{1} + r_{2}$
Hence, the number of common tangents are2