Which equation represents a hyperbola with a center at (0, 0), a vertex at (−48, 0), and a focus at (50, 0)?

The center, vertex, and focus all lie on the line y = 0. Then we know that the equation of a hyperbola is a^2 + b^2 = c^2 . a^2 represents the x part of the equation and the y part will be subtracted. We know that the vertex is 48 units from the center and that the focus is 50 units from the center. Then we have that b^2 = 2500 - 2304 = 196 . Thus the equation that represents the hyperbola is x^2/2304 - y^2/196 = 1 or 49x^2 -576y^2 - 112896 = 0

You just need to add 32 to 14 and get 46.