In an ellipse the sum of the focal distances is constant; and in an hyperbola the difference of the focal distances is constant.
An oval is never mistaken for a circle, nor an hyperbola for an ellipsis.
But after you have demonstrated to him the properties of the hyperbola and its asymptote, the apparent absurdity vanishes.
The curve is in this case called an hyperbola (see fig. 20).
In the hyperbola we have the mathematical demonstration of the error of an axiom.
The axes of an hyperbola bisect the angles between the asymptotes.
These curves—the ellipse, the parabola, hyperbola—play a large part in the subsequent history of astronomy and mechanics.
Two of the sides of the triangle in this proposition constitute a special form of the hyperbola.
If the cone is cut off vertically on the dotted line, A, the curve is a hyperbola.
With a certain speed it will assume the parabola, and with a greater the hyperbola.
1660s, from Latinized form of Greek hyperbole "extravagance," literally "a throwing beyond" (see hyperbole). Perhaps so called because the inclination of the plane to the base of the cone exceeds that of the side of the cone.
In geometry, a curve having a single bend, with lines going infinitely far from the bend.
Note: The path of a comet that enters the solar system and then leaves forever is a hyperbolic curve (half of a hyperbola).