Microphones are placed at points (-c, 0) and (c, 0). An explosion occurs at point P(x, y) having positive x-coordinate. See the figure. The sound is detected at the closer microphone t seconds before being detected at the farther microphone. Assume that sound travels at a speed of 330 m per sec, and show that P must be on the following hyperbola.

x2 y2 3302r? 330212 4 4c2 33012 y , ) %3D (-c, 0) (c, 0)