Question 633382
Find the foci of the hyperbola. 
y^(2)-9x^(2)-4y-54x-86=0
complete the square
y^2-4y-9x^2-54x-86=0
(y^2-4y+4)-9(x^2+6x+9)=86+4-81
(y-2)^2-9(x+3)^2=9
{{{(y-2)^2/9-(x+3)^2/1=1}}}
This is an equation of a hyperbola with vertical transverse axis.
Its standard form: {{{(y-k)^2/a^2-(x-h)^2/b^2=1}}}
For given equation:
center: (-3,2)
a^2=9
b^2=1
c^2=a^2+b^2=9+1=10
c=√10≈3.2
foci: (-3, 2±c)=(-3,2±3.2)=(-3+5.2) and (-3,-1.2)