Hyperbola definitions and example sentences on Wordnik

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Definitions (18)

American Heritage Dictionary (1)

noun A plane curve having two branches, formed by the intersection of a plane with both halves of a right circular cone at an angle parallel to the axis of the cone. It is the locus of points for which the difference of the distances from two given points is a constant.

Century Dictionary (15)

A curve formed by the intersection of a plane with a double cone—that is, with two similar cones placed vertex to vertex, so that one is the continuation of the other. If the plane cuts only one of the cones, the section is a circle, an ellipse, or a parabola; but if both cones are cut, the section is a hyperbola. A hyperbola may be formed by throwing upon a table the shadow of a ball the top of which is higher than the source of light. It has two asymptotes. If through any point of the curve lines be drawn parallel to the asymptotes, the parallelogram so formed will be of constant area for any given hyperbola. The point of intersection of the asymptotes is the center of the hyperbola, and is equidistant from the two intersections of any line through it with the hyperbola. The two lines through the Center bisecting the angles of the asymptotes are the linesof the axes of the hyperbola, and the curve is symmetrical with respect to each of these. One of these lines cuts the curve, and the points of intersection are called the vertices of the hyperbola. The line between the vertices is the major or transverse axis of the hyperbola. If from the vertices lines be drawn parallel to the two asymptotes, the two points at which these lines will meet will be the extremities of the minor or conjugate axis. Although the axes bear these names, the minor may be longer than the major axis. The equation of the hyperbola, referred to its center and axes, is The foci'of the hyperbola are two points on the line of the transverse axis distant from the center as far as the vertices are from the extremities of the conjugate axis. If from any point of the curve lines be drawn to the two foci, the difference of the lengths of these lines is constant for any given hyperbola, and the angle between them is bisected by the tangent at that point. The eccentricity of the hyperbola is the secant of half the angle between the asymptotes. The parameter or latus rectum of a hyperbola is a chord through the focus perpendicular to the transverse axis.
An algebraic curve having asymptotes greater in number by one than its order. This meaning was introduced by Newton.
Acute hyperbola a hyperbola which lies in the acute angle between its asymptotes. Ambigenal, anguineal, etc., hyperbola. See the adjectives.

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Wouldn't hyperbola (truthfully) merely "tolerate" any Jews who declare their disdain for Israel? — Propeller Most Popular Stories
Inverse Relationship plotted on the y-axis (hyperbola) y = k / x — Recently Uploaded Slideshows
Write an equation for the hyperbola with vertices (- 10,1) and (6,1) and foci (- 12,1) and (8,1) mutiple answers? — Yahoo! Answers: Latest Questions
AND, at the same time hyperbola is also right on the button here also. — Propeller Most Popular Stories
- We know this wasn't true under previous administration. hyperbola - Another hyperbolic statement. — Propeller Most Popular Stories

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Etymologies (2)

American Heritage Dictionary (1)

New Latin, from Greek huperbolē, a throwing beyond, excess (from the relationship between the line joining the vertices of a conic and the line through its focus and parallel to its directrix); see hyperbole.

Century Dictionary (1)

= French hyperbole = Spanish hipérbola = Portuguese hyperbole = Italian iperbola, from New Latin hyperbola, from Greek ὑπερβολή, the conic section hyperbola (so called by Apollonius because the side of the rectangle on the abscissa equal to the square of the ordinate overlaps the latus rectum) (see ellipse), literally excess (see hyperbole), from ὑπερβάλλειν, throw over, exceed, from ὑπέρ, over, +βάλ λειν,throw.

hyperbola

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