Alan Horwitz, A ladder ellipse problem,
Forum Geometricorum, 16 (2016) 63--67.
Abstract. We consider a problem similar to the well-known ladder box problem, but where the box is replaced by an ellipse. A ladder of a given length, s, with ends on the positive x- and y- axes, is known to touch an ellipse that lies in the first quadrant and is tangent to the positive x- and y-axes. We then want to find the height of the top of the ladder above the floor. We show that there is a value, s = s_0, such that there is only one possible position of the ladder, while if s > s_0, then there are two different possible positions of the ladder. Our solution involves solving an equation which is equivalent to a 4-th degree polynomial equation.
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