Final answer:
The given equation represents a hyperbola with center at (4,5), vertices at (0,5) and (8,5), and b = 2.
Step-by-step explanation:
The given equation represents a hyperbola with center at (4,5), vertices at (0,5) and (8,5), and b = 2. The standard form of the equation for a hyperbola with center (h,k), and major axis along the x-axis is [(x-h)^2/a^2] - [(y-k)^2/b^2] = 1, where a represents the distance between the center and the vertices along the x-axis, and b represents the distance between the center and the foci along the y-axis.
Comparing the given equation (x-4/16)^2 - (y-5/4)^2 = 1 to the standard form equation, we can determine that a = 4/4 = 1, and b = 2.
Therefore, the equation represents a hyperbola with center (4,5), major axis of length 2a = 2(1) = 2, and minor axis of length 2b = 2(2) = 4.