Answer
See below
Work Step by Step
Given: $9y^2-x^2-54y+8x+56=0$
We can see that $a=-1\\b=0\\c=9$
We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(-1)(9)\\=36$
Since $36\gt0$, the conic is a hyperbola.
To graph the hyperbola, first complete the square:
$9y^2-x^2-54y+8x+56=0\\-x^2+8x+9y^2-54y=56\\-(x^2-8x+16)+16+9(y^2-6y+9)-81=-56\\-(x-4)^2+9(y-3)^2=9\\\frac{(y-3)^2}{1}-\frac{(x-4)^2}{9}=1$
From the equation, you can see that the center is at $(4,3)$
