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.

Question

02-08-2021
Mathematics

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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.

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