Photography m fixed point

When n = 1, the trajectory is the middle vertical line connecting M 1 and M2.

When n≠ 1, the trajectory is a circle called Apollonius circle, which is one of the famous trajectories. Take a point A on the line between M 1 and M2, so that M 1A = n * M2A. Then take a point b from the extension line of the straight line M 1M2 (when 0 < n < 1, it is a reverse extension line), so that M 1b = n * m2b. Make a circle with AB as the diameter, and this circle is the locus of finding (please prove it yourself).

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