Answer
vertex $(1,3)$, focus $(1,\frac{7}{2})$.
Work Step by Step
$x^2-2x-2y+7=0$,
$x^2-2x=2y-7$,
$x^2-2x+1=2y-6$,
$(x-1)^2=2(y-3)$,
$(x-1)^2=4(\frac{1}{2})(y-3)$,
thus we have the vertex $(1,3)$, parabola opens up,
$p=\frac{1}{2}$, focus $(1,\frac{7}{2})$.
