As the vertex is $(1,1)$ and focus is $(3,1)$,
whose ordinate is same its axis of symmetry is $y =1$.
And as vertex is equidistant from foci and directrix,
and latter is perpendicular to axis of symmetry.
Directrix is $x =1$
As parabola is the locus of a point whose distance from directrix $x +1=0$ and focus $(3,1)$
Its equation is $(x-3)^{2}+(y-1)^{2}=(x+1)^{2}$
$\Rightarrow x ^{2}-6 X +9+ y ^{2}-2 Y +1= x ^{2}+2 X +1 $
$\Rightarrow y ^{2}-2 y +9=8 x$
$\Rightarrow ( y -1)^{2}=8( x -1)$