A telescope contains both a parabolic mirror and a hyperbolic mirror. They share focus F1​, which is 46 feet above the vertex of the parabola. The​ hyperbola's second focus F2 is 8 ft above the​ parabola's vertex. The vertex of the hyperbolic mirror is 2 ft below F1. 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.