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.

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x2 y2 3302r? 330212 4 4c2 – 330²12 y Рх, у) %3D (-c, 0) х (c, 0)