We set the entrance to be the origin of a coordinate system. One leg of the new hiking loop is a parabola that starts at the entrance and has its most northern point at 1km East and 4km North from the entrance. The other leg of the loop is also shaped like a parabola section. It starts 0.5 km south of the entrance and has its southern most point 1km east and 1km south from the entrance. The path ends where the legs meet (West of the entrance). Where will that be?