Question 816974
9x^2+25y^2-36x+50y-164=0 
rearrange terms:
9x^2-36x+25y^2+50y=164
complete the square:
9(x^2-4x+4)+25(y^2+2y+1)=164+36+25
9(x-2)^2+25(y+1)^2=225
{{{(x-2)^2/25+(y+1)^2/9=1}}}
This is an equation of an ellipse with horizontal major axis.
Its standard form of equation: {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}, (h,k)=(x,y) coordinates of center.
For given ellipse:
center: (2,-1)
a^2=25
b^2=9