EPTSo, the question:
You have two sound receivers, 1 and 2. One detects a sound t seconds after the other. Assume that the speed of sound propagation is constant throughout this made up world. What curve decribes the possible locations of the sound source? Assumed 2D.
+ Show Spoiler [solution] +
By symmetry and a distinct closer point, it follows that it must either be a parabola or a hyperbola. The definition of a hyperbola is "A hyperbola may be defined equivalently as the locus of points where the difference of the distances to the two foci is a constant equal to 2a, the distance between its two vertices.", thus the solution is half a hyperbola.
Of course it'd be faster if you randomly knew the foci definition of a hyperbola off the top of your head XD
