What is the equation of a hyperbola with a = 6 and c = 8? Assume that the transverse axis is horizontal.

The standard equation for a hyperbola with a horizontal transverse axis is

(x-h) ^2/a^2 - (y-k) ^2/b^2 = 1. The center is at (h, k). The distance between the vertices is 2a. The distance between the foci is 2c and c^2 = a^2 + b^2. Therefore,

8^2 = 6^2 + b^2

b = 2 √7

Assuming it is located at the origin.

(x-h) ^2/a^2 - (y-k) ^2/b^2 = 1

(x) ^2/6^2 - (y) ^2 / (2√7) ^2 = 1

x^2/36 - y^2/28 = 1