Explanation

(b)
Equation of family of concentric circles to the circle $x^{2} + y^{2} + 6x + 8y - 5 = 0$ is $x^{2} + y^{2} + 6x + 8y + \lambda = 0$ which is similar to$x^{2} + y^{2} + 2gx + 2fy + c = 0$. Since, it is equation of concentric circle to the circle$x^{2} + y^{2} + 6x + 8y - 5 = 0$. Thus, the point $( - 3,\ 2)$ lies on the circle $x^{2} + y^{2} + 6x + 8y + c = 0$
$\Rightarrow ( - 3)^{2} + (2)^{2} + 6( - 3) + 8(2) + c = 0$
$\Rightarrow 9 + 4 - 18 + 16 + c = 0$
$\Rightarrow c = - 11$