Since the vertices and foci lie on the same horizontal line, the hyperbola is oriented horizontally. This helps us determine that the x2 term in the equation will be the positive one, the y2 term the negative. We need to calculate where the center is, and what are the values for a and b, since a2 is the denominator of the positive squared term in the equation, while b2 is the denominator of the negative. a gives the distance from center to vertex, b gives the distance from center to "co-vertices" (analogous to an ellipse, though these don't lie on the conic as they do in the ellipse -- instead, we use them and the vertices to create a rectangle, the diagonals of which are the asymptotes of the hyperbola). Lastly, we have c2 = a2 + b2 , where c is the distance from the center to the foci:
The midpoint between the two foci is the center, (0 , 0). The distance from the center to a vertex is 4, so a = 4. The distance from the center to a focus is 5. So 52 = 42 + b2 , and b = 3.
x2 / 16 - y2 / 9 = 1
