Question 9378
25x^2 - 144y^2 = 3600

 Divide both sides by 3600 and simplify

 x^2/144 - y^2/25 = 1

 This is the equation of a hyperbola.

 In general x^/a^2 - y^2/b^2 = 1 is the equation of a hyperbola for nonzero a and b

 In its derivation the quantity b^2 = c^2 - a^2 where c is the x coordinate of a focus.

 We have a^2 = 144 and b^2 = 25

 So c^2 = a^2 + b^2

         = 169

 So the hyperbola x^2/144 - y^2/25 = 1 has foci at (-c,0) and (c,0)

 In other words foci at (-13,0) and (13,0)