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

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