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

Answer 2

Yes, that's perfectly correct. Although there might be a bit estimation error here. You might want to take exact value of b. If it is an exam, you also might want to present your answer in same number of significant figures as in question.