Final answer:
The center of the hyperbola is (0,0). The vertices are (0,4) and (0,-4). The equations of the asymptotes are y = (4/3)x and y = -(4/3)x.
Step-by-step explanation:
A hyperbola can be represented by the equation (x-h)^2/a^2 - (y-k)^2/b^2 = 1, where (h,k) represents the center of the hyperbola. Comparing this equation with the given equation, we have (x-0)^2/12 - (y-0)^2/16 = 1. Therefore, the center of the hyperbola is (0,0).
To find the vertices, we can use the formula a^2 = h^2 + k^2. Substitute the values of a^2 and the center coordinates, we get 12 = 0^2 + 0^2. Therefore, the vertices are (0,4) and (0,-4).
The equation of asymptotes for a hyperbola in standard form is given by y = ±(b/a)x + k, where (h,k) represents the center. Substituting the values of a, b, h, and k, we get the equations of the asymptotes as y = (4/3)x and y = -(4/3)x.