Answer
See below
Work Step by Step
Given $4x^2-16y^2-56x+160y-268=0$
Rewrite as: $4(x^2-16x)-16(y^2-10y)-268=0\\4(x^2-16x+64)-256-16(y^2-10y+25)+400-268=0\\4(x-8)^2-16(y-5)^2=124\\\rightarrow \frac{(x-8)^2}{31}-\frac{(y-5)^2}{7.75}=1$
Compare the given equation to the standard form of an equation of a hyperbola.
