Ladder Day Question

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 [with] 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 anywhere on the ladder.

The Mathematical Correspondent, Volume 1, 1804

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The answer is: if \(a\) is the distance from the point to the top of the ladder, and \(b\) is the distance from the point to the bottom of the ladder, then the equation is \(\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2}=1\), an ellipse (or a circle if \(a = b\))

"Ladder Day Question," Convergence (July 2006)

Convergence