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 the center of the hyperbola is the origin and the transverse axis is horizontal.

Answer 1

Answer:

$\frac{x^2}{55000^2} - \frac{y^2}{59464^2} =1$

Step-by-step explanation:

the transverse axis is horizontal.

so its a horizontal hyperbola

Center is the origin so center is (0,0)

Equation of horizontal hyperbola is

$\frac{x^2}{a^2} - \frac{y^2}{b^2} =1$

Given a= 55000 and c= 81000

c^2 = a^2 + b^2

81000^2 = 55000^2 + b^2

subtract 55000^2 on both sides

b  = sqrt(81000^2 - 55000^2)= 59464.27

now plug in the values

$\frac{x^2}{55000^2} - \frac{y^2}{59464^2} =1$