Answer to Question #269939 in Analytic Geometry for Elay

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 point P(x,y)- the location of the ship.

If the signal from N was received by the ship four seconds before the signal it received from M, it means, that the distance between P and M is more than between P and N by:

0.33*4=1.32.

The distance between P and M:

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

The distance between P and N:

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

Then:

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

This curve shows the possible location of the ship.