Final answer:
The given equation defines a hyperbola because after completing the square and simplifying, the equation is characterized by having opposite signs in front of the x² and y² terms.
Step-by-step explanation:
The type of conic section defined by the equation 16x²-4y²+96x-16y+64=0 can be determined by completing the square for both x and y terms. After rearranging, we can rewrite the equation as (4x² + 96x) - (y² + 16y) = -64. Dividing the entire equation by -4 to simplify and to get a positive y² term, we have -4x² - 96x + y² + 16y = 64, which can further be simplified by completing the square for both x and y terms, resulting in a hyperbola. This is because the signs in front of the x² and y² terms are different, which is a characteristic of a hyperbola. Thus, the given equation represents a hyperbola.