Answer:
The standard form of the equation of a hyperbola with horizontal axis is:(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1where (h, k) is the center of the hyperbola, a is the distance from the center to each vertex, and b is the distance from the center to each co-vertex.Using the given information, we can determine the values of h, k, a, and b:The center is (5, -6), so h = 5 and k = -6.The distance from the center to each vertex is 5, so a = 5.The distance from the center to each co-vertex is not given, but we know that the point (15, 0) lies on the hyperbola. Since this point is 10 units to the right of the center, we can assume that b is 10.Substituting these values into the standard form, we get:(x - 5)^2 / 5^2 - (y + 6)^2 / 10^2 = 1Simplifying, we get:(x - 5)^2 / 25 - (y + 6)^2 / 100 = 1Therefore, the equation of the hyperbola is:(x - 5)^2 / 25 - (y + 6)^2 / 100 = 1.