Explanation

(b)
The centre and radii of two circles are $C_{1}(1,\ - 3),\ C_{2}\left( \frac{5}{2},\ - 3 \right)$
And $r_{1} = \sqrt{1 + 9 - 6} = 2,$
$r_{2} = \sqrt{\frac{25}{4} + 9 - 15} = \frac{1}{2}$
Now, $C_{1}C_{2} = \sqrt{\left( 1 - \frac{5}{2} \right) + ( - 3 + 3)^{2}} = \frac{3}{2}$
And different of radii$= 2 - \frac{1}{2} = \frac{3}{2}$
Since, the distance between their centres is equal to the difference of their radii.
$\therefore$ The circles touch each other internally.