Explanation

(b)
We have, $\frac{dy}{dx} = \frac{ax + g}{by + f}$
$\Rightarrow$ $(by + f)dy = (ax + g)dx$
On integrating, we get
$\frac{by^{2}}{2} + fy = \frac{ax^{2}}{2} + gx + c$
$\Rightarrow$ $ax^{2} - by^{2} + 2gx - 2fy + c = 0$
This represents a circle, if $a = - b$