What is a rectangular hyperbola?

How is it proven that a certain line on a graph is a rectangular hyperbola?

Thanks

Rectangular Hyperbola (also known as equilateral hyperbolas or right hyperbolas) are 'C'-shaped curves. In these curves, the vertical and the horizontal portions (of the curves) get closer to the y-axis and x-axis as we move vertically upwards and horizontally rightwards. But, both the portions of a rectangular hyperbola never ever touch any of the axes of the graph.

In the syllabus and chapters of Economics XII, we deal with only two curves that can be regarded as a rectangular hyperbola namely, the demand curve and the AFC curve. (Note: a point to be kept in mind is that the demand curve can be a straight line or a downward sloping curve as well.)