Explanation

(b)
Equation of the line $\frac{ax}{c - 1} + \frac{by}{c - 1} + 1 = 0$ has two independent parameters. It can
pass through a fixed point if it contains only one independent parameter. Now , there must be one relation between $\frac{a}{c - 1}\ and\frac{b}{c - 1}$ independent of $a,\ b$ and $c$ so that $\frac{a}{c - 1}$ can be expressed in terms of $\frac{b}{c - 1}$ and straight line contains only one independent parameter. Now, that given relation can be expressed as $\frac{5a}{c - 1} + \frac{4b}{c - 1} = \frac{t - 20c}{c - 1}$ RHS in independent of $c$ if $t = 20$