Hyperbolas

A Ship navigator ca plot the location of a ship by using a radio navigation system called LORAN(Long Range Navigation). In this system, a pair of radio sending stations continually transmit signals at different time intervals. The navigator measures the difference in time between the two signals received and then used this information to plot the path of the ship. Its curved path called hyperbola. The signals from another pair of stations are used to plot a second hyperbolic path. The intersection of the two hyperbolas determines the exact position of the ship.

In the diagram above, the sending stations are represented by two fixed points, F1 and F2 and the ship by the point P. the ship P move along a path that maintains the constant difference between the distances from the point P to the fixed points. The difference PF1 – PF2 is the same for all the position of P.

A hyperbola is the set of all points P in the plane such that the difference between the distances from P to two fixed points is given constant.

Each fixed points are called Focus, if the P is the point on the hyperbola and F1 and F2 are foci. Then PF1 and PF2 are the focal radii.