Verified answer

standard form of hyperbola (horizontal axis)

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

asymptote slope m = ± b/a

standard form of hyperbola (vertical axis)

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

asymptote slope m = ± a/b

(h,k) => center

a: distance between center and vertices

c^2 = a^2 + b^2

c: distance between center and focus

......................................................................................

vertices (3,-4) and (7,-4) => center: (5, -4), a = 2

foci at (5±√29,-4) => c = √29

b^2 = 25

(x-5)^2 / 4 - (y+4)^2 / 25 = 1

http://www.wolframalpha.com/input/?i=plot%3A+%28x-...