Final answer:
The equation that represents the hyperbola shown in the graph is option D: y-1^2/64 - x-3^2/36=1.
Step-by-step explanation:
The equation that represents the hyperbola shown in the graph is option D: y-1^2/64 - x-3^2/36=1.
A hyperbola is a set of points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix). The equation of a hyperbola in standard form is (x-h)^2/a^2 - (y-k)^2/b^2 = 1 for a horizontal hyperbola or (y-k)^2/a^2 - (x-h)^2/b^2 = 1 for a vertical hyperbola.
In option D, the equation is in the form (y-k)^2/a^2 - (x-h)^2/b^2 = 1, where k = 1, h = 3, a^2 = 36, and b^2 = 64. This matches the equation of the hyperbola shown in the graph.