Question

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.

Answer 1

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

Answer 2

Answer:

x^2/5500^2-y^2/(3536000000)=1

Step-by-step explanation:

c^2=a^2+b^2   81000^2=55000^2+b^2

b^2=3536000000, b=4000sqrt(221)