Question

Two stations, located at M (−1.5, 0) and N (1.5, 0) (units are in km), simultaneously send sound signals to a ship, with the signal traveling at the speed of 0.33 km/s. If the signal from N was received by the ship four seconds before the signal it received from M, find the equation of the curve containing the possible location of the ship. 

Answer 1

Let P(x,y) be the location of the ship.

If the signal from N was received by the ship 4s before the signal it received from M then the distance between P and M is more than the distance between P and N by:0.33*4=1.32

Distance between P and M=$\sqrt{(x-1.5)^2+y^2}$

Distance between P and N=$\sqrt{(x+1.5)^2+y^2}$

Distance PM- Distance PN=1.32

$\sqrt{(x-1.5)^2+y^2}-\sqrt{(x+1.5)^2+y^2}=1.32$

This is the equation of the curve showing the possible location of the ship.