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

Given:

Hyperbola

a=55,000 km and c=81,000 km

hyperbola is the origin and the transverse axis is horizontal

Required:

Equation of the path of a satellite

Solution:

Formula for hyperbola, (x-h) 2/a2 - (x-k) 2/b2 = 1

At origin, (h, k) = (0, 0)

(x-0) 2 / (55000) 2 - (x-0) 2 / (81000) 2 = 1

X2/12100 - y2/26244 = 250000