Certain telescopes contain both parabolic mirror and a hyperbolic mirror. In the telescope shown in figure the parabola and hyperbola share focus `F_(1)` which is 14m above the vertex of the parabola. The hyperbola's second focus `F_(2)` is 2m above the parabola's vertex. The vertex of the hyperbolic mirror is 1m below `F_(1)`. Position a coordinate systemm with the origin at the centre of the hyperbola and with the foci on the y-axis. then find the equation of the hyperbola.