Answer
See below
Work Step by Step
Given $9x^2-4y^2-36x-32y-64=0$
We can see that $a=9\\b=0\\c=4$
We will find the discriminant of the given equation $=b^2-4ac\\=0^2-4(9)(4)\\=144$
Since $144 \gt0$, the conic is a hyperbola.
To graph the hyperbola, first complete the square in x.
$9x^2-4y^2-36x-32y-64=0\\9(x^2-4x+4)-36-4(y+8y+16)+64=64\\9(x-2)^2-4(y+4)^2=36\\\frac{(x-2)^2}{4}-\frac{(y+4)^2}{9}=1$
From the equation, you can see that the center is at $(2,-4)$ and the vertices are at $(0,-4)$ or $(4,-4)$
