jmc

Question

In a certain hyperbola, the center is at (2,0), one focus is at (2,6), and one vertex is at (2,-3). The equation of this hyperbola can be written as (y - k)^2a^2 - (x - h)^2b^2 = 1.Find h + k + a + b.

Accepted Answer

The center of the hyperbola is (h,k) = (2,0). The distance between the center and one vertex is a = 3, and the distance between the center and one focus is c = 6. Then b^2 = c^2 - a^2 = 6^2 - 3^2 = 27, so b = 3 3. Therefore, h + k + a + b = 2 + 0 + 3 + 3 3 = 3 3 + 5.