Two LORAN radio stations A and B are 140 kilometers apart and send a simultaneous radio signal to a ship. The signal from B arrives 0.0003 seconds before the signal from A. If the signal travels 300,000 kilometers per second, find the equation of the hyperbola on which the ship is positioned. Use a coordinate system where the origin is the midpoint between the stations, and the stations lie on the x- axis.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 44E: By definition, a hyperbola is the locus of points whose positive difference of distances from two...
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Two LORAN radio stations A and B are 140 kilometers apart
and send a simultaneous radio signal to a ship.
A
The signal from B arrives 0.0003 seconds before the signal
from A. If the signal travels 300,000 kilometers per second,
find the equation of the hyperbola on which the ship is
positioned. Use a coordinate system where the origin is the
midpoint between the stations, and the stations lie on the x-
axis.
Transcribed Image Text:Two LORAN radio stations A and B are 140 kilometers apart and send a simultaneous radio signal to a ship. A The signal from B arrives 0.0003 seconds before the signal from A. If the signal travels 300,000 kilometers per second, find the equation of the hyperbola on which the ship is positioned. Use a coordinate system where the origin is the midpoint between the stations, and the stations lie on the x- axis.
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