Question

Write the equation of a hyperbola with the given information:

Vertices: (4, 11) and (4, -13)
Foci: (4, -1 + √194) and (4, -1 - √194)

A. (x - 4)^2 / 194 - (y - 1)^2 / 144 = 1

B. (x - 4)^2 / 144 - (y + 1)^2 / 194 = 1

C. (x - 4)^2 / 194 - (y + 1)^2 / 144 = 1

D. (x - 4)^2 / 144 - (y - 1)^2 / 194 = 1

Answer 1

The equation of the hyperbola is (x - 4)^2 / 144 - (y + 1)^2 / 194 = 1.

Step-by-step explanation:

The equation of a hyperbola with the given information can be determined by using the formula: (x - h)^2 / a^2 - (y - k)^2 / b^2 = 1, where (h, k) is the center of the hyperbola, and 'a' and 'b' are the distances from the center to the vertices.

In this case, the center of the hyperbola is (4, -1). The distance from the center to the vertices is 12 (11 - (-1)), so 'a' is 12. The distance from the center to the foci is √194, so 'b' is √194.

Substituting these values into the equation, we get: (x - 4)^2 / 144 - (y + 1)^2 / 194 = 1. Therefore, the correct option is B.