equation of a hyperbola

Question

Precalculus Question:

Two radar sites are tracking an airplane that is flying on a hyperbolic path. The first radar site is located at (0,0), and shows the airplane to be 200 meters away at a certain time. The second radar site, located 160 miles east of the first, shows the airplane to be 100 meters away at this same time. Find the coordinates of all possible points where the airplane could be located. (Find the equation of the hyperbola where the plane could be located).

Answer 1

Let 2 c = 160 mi then c =80 mi the difference in distance between the two radar sites measurement is

200-100= 100 mi then 2 a = 100 mi and a= 50 mi.

c^2 = a^2 + b^2 so b^2= 6400 - 2500 = 3900

Equation of the hyperbola is x^2/2500 -y^2/3900 =1