Poncelet Brianchon Hyperbola Problem

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If a rectangular hyperbola circumscribes a triangle, it will also pass through the orthocenter of the triangle.
A rectangular hyperbola has asymptotes at right angles. We can rotate it so that the asymptotes are the axes, and thus the equation of the hyperbola is XY=a. This can be represented as the function Y=a/X, and it is convenient to use the function for this example rather than the conic, as Geometry Expressions parameterizes the function by x coordinate rather than by an angle, and this generates simpler expressions.

We see from the diagram that point D satisfies the equation XY=a.

Expressions

Name Input
Point D Eq Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image