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Watch That Ladder

A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall. If the base of the ladder be drawn along the horizontal plane, in a direction perpendicular to the plane of the wall the top of the ladder sliding downwards, against the wall; it is required to find the equation of the curve which is the locus of a point taken any where on the ladder.

Note: For a corresponding problem, see the Problem-of-the-Week section.

Solution:

Source: The Mathematical Correspondent, 1804 (America's first mathematics journal)