hyperbola

[ hahy-pur-buh-luh ]

noun

, Geometry.

1. the set of points in a plane whose distances to two fixed points in the plane have a constant difference; a curve consisting of two distinct and similar branches, formed by the intersection of a plane with a right circular cone when the plane makes a greater angle with the base than does the generator of the cone. Equation: x 2 /a 2 − y 2 /b 2 = ±1.

hyperbola

/ haɪˈpɜːbələ /

noun

1. a conic section formed by a plane that cuts both bases of a cone; it consists of two branches asymptotic to two intersecting fixed lines and has two foci. Standard equation: x ²/ a ² – y ²/ b ² = 1 where 2 a is the distance between the two intersections with the x -axis and b = a √( e ² – 1), where e is the eccentricity

hyperbola

/ hī-pûr′bə-lə /

, Plural hyperbolas hī-pûr′bə-lē

1. A plane curve having two separate parts or branches, formed when two cones that point toward one another are intersected by a plane that is parallel to the axes of the cones.

hyperbola

1. In geometry , a curve having a single bend, with lines going infinitely far from the bend.

Notes

The path of a comet that enters the solar system and then leaves forever is a hyperbolic curve (half of a hyperbola).

Word History and Origins

Origin of hyperbola¹

1660–70; < New Latin < Greek hyperbolḗ the geometrical term, literally, excess. See hyperbole

Word History and Origins

Origin of hyperbola¹

C17: from Greek huperbolē, literally: excess, extravagance, from hyper- + ballein to throw

Example Sentences

The fact that every circle, ellipse, parabola and hyperbola that can be drawn can be described by a quadratic equation in x’s and y’s is helpful for science because all of these curves are found in the real world.

From Literature

The ellipse is the curve that describes how planets orbit around the sun, and the path followed by the shadow of the tip of a sundial during a day is a hyperbola.

From Literature

By contrast, equations with quadratic terms—ones that include values for x2 and/or y2—always produce one of the following four types of curve: circle, ellipse, parabola or hyperbola.

From Literature

"Not every hyperbola is a burial or a grave — there's tree roots, there's masses, and other things in the substrate," Small says.

From Salon

It placed several satellites into orbit around Earth, including a radio satellite developed by an amateur radio group and the Beijing Institute of Technology. i-Space hopes that Hyperbola rockets will help to bolster China’s burgeoning commercial space industry.

From Nature

Related Words

• arc
• arch
• contour
• loop
• trajectory