A telescope contains both a parabolic mirror and a hyperbolic mirror. They share focus Upper F 1, which is 45 feet above the vertex of the parabola. The hyperbola's second focus Upper F 2 is 9 ft above the parabola's vertex. The vertex of the hyperbolic mirror is 4 ft below Upper F 1. Find the equation of the hyperbola if the center is at the origin of a coordinate system and the foci are on the y-axis.