Question

Find an equation that models the path of a satellite if its path is a hyperbole, a = 55,000 km, and c = 81,000 km. Assume that the center of the hyperbole is the origin and the transverse axis is horizontal.

Answer 1

Vertex(55,000,0)
Focus (81,000,0)
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c^2 = a^2 + b^2
81000^2 = 55,000^2 + b^2

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b = 59464.27
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Form: [x^2/a^2] - [y^2/b^2] = 1
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x^2/55,000^2 - y^2/59464^2 = 1