Consider a line, the x-axis say, and a point A(a_{x},a_{y}) 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

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 (OF_{1}/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.