Answer
$-1$
Work Step by Step
General form of a horizontal parabola is given as: $(x-h)^2=4p(y-k)$...(1)
Here, $\text{Vertex}=(h,k)$ and focus is: $(h, k+p)$
As we are given $(x-2)^2=8(y-1)$
From equation (1), we get: $h=2,k=1$ and $4p=8\implies p=2$
$\text{Vertex}=(h,k) \implies (1,1)$
Also, focus is: $(h,k+p) \implies f(2,1+2)=f(2,3)$
Directrix is: $y=k-p \implies y=1-2=-1$
Hence, Directrix is: $y=-1$
