The parabola $(y+1{)}^2=a(x-2)$ passes through the point (1,-2).The equation of its directrix is

$(y+1{)}^2=a(x-2)$. Since it passes through $(1,-2)$ we get $(-2+1{)}^2=a(1-2)\Rightarrow -a=1$

$$\begin{gathered} \Rightarrow a=-1. \\ \therefore L.L.R 4A=-1\Rightarrow A=\frac{-1}{4} \end{gathered}$$

Equation of directrix is $x-h+A=0\Rightarrow x-2-\frac{1}{4}=0\Rightarrow 4x-9=0$