Question

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

Answer 1

My work:

a^2 + b^2 = c^2
55,000^2 + b^2 = 81,000^2
b = 59464.27

(x^2/a^2) - (y^2/b^2) = 1
x^2/55,000^2 - y^2/59464^2 = 1
x^2/3,025,000,000 - y^2/3,535,967,296 = 1