In example 3 on pages 573 and 574, you were examining the locus of points equidistant from two given points. We will investigate the locus below.
In the sketch below are three points A, B and P. Notice that as you move P the distance between P and the two other points is the same, that is, PA = PB. Can you spot any relationship between the path of P and the two points A and B? P may be traced by clicking on the Trace button. At any point, after you have started tracing, you may erase the traced points by clicking on the red X in the bottom right corner of the screen. Once you think you have the relationship, move A and B to new positions and see if your conjecture holds for this new arrangement.
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