[alogo] Rectangular hyperbola simply defined

Consider a line, the x-axis say, and a point A(ax,ay) outside it. Measure the distance y=|AB| as a function of the abscissa x of a moving point B(x,0) on the line. The graph is a rectangular hyperbola (part of it) with equation

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The figure shows the foci, which are on line and, as always with rectangular hyperbolas, the distance of its center from the focus and its vertex A satisfies (OF1/OA)2 = 2. The figure illustrates the fact that the distance AO from the line is shorter than any other segment AB, for B on the line. The graph passes through A and has there a minimum. Every rectangular hyperbola has such an interpretation. The hyperbola changes its shape by moving point A.

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