Question 307008
You need to complete the square in x and y.
{{{ 16y^2-9x^2+36x-32y-164=0}}}
{{{-9x^2+36x+16y^2-32y-164=0}}}
{{{-9(x^2-4x)+16(y^2-2y)=164}}}
{{{-9(x^2-4x+4)+16(y^2-2y+1)=164-36+16}}}
{{{-9(x-2)^2+16(y-1)^2=144}}}
{{{(y-1)^2/9-(x-2)^2/16=1 }}}
Unequal coefficients for {{{x^2}}} and {{{y^2}}} and unequal signs are the signs of a hyperbola. 
There now you can solve for center and foci.