Answer
Vertex: $(4,-6), (-2,6)$ and center: $(1,-6)$
Focus: $(1+\sqrt 6, -6), (1 -\sqrt 6, -6)$
Work Step by Step
The standard form of the equation of the circle is:
$(x^2-2x+1)+3(y^2+12y+36)=-100+1+108$
or, $(x-1)^2+3(y+6)^2=9$
So, we see that the vertex is: $(h \pm a , k)=(4,-6), (-2,6)$
The center is: $(1,-6)$
$c=\sqrt {a^2-b^2}=\sqrt{6}$
Focus: $(h \pm c , k)=(1+\sqrt 6, -6), (1 -\sqrt 6, -6)$
