Conic Sections Question

Question

Tricky 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.

 

A little help would be wonderful!

Thank you :)

Answer 1

The form of the equation is ((x-0)²)/a² - ((y-0)²)/b² = 1 plugging the data and calculating b which comes to be 59400 km c=√(a² + b²). we know a and c so we may calculate b

The final equation will be ((x²)/(3025*10^6)) + ((y²)/(3528.36*10^6) =1

Check!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!