  # Hyperbola vs. Hyperbolic — What's the Difference? ## Definitions

#### Hyperbola➦

In mathematics, a hyperbola (listen) (adjective form hyperbolic, listen) (plural hyperbolas, or hyperbolae (listen)) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

#### Hyperbolic➦

Of, relating to, or employing hyperbole.

#### Hyperbola➦

A symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

#### Hyperbolic➦

Of, relating to, or having the form of a hyperbola.

#### Hyperbola➦

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.

#### Hyperbolic➦

Of or relating to a geometric system in which two or more lines can be drawn through any point in a plane and not intersect a given line in the plane.

#### Hyperbola➦

(geometry) A conic section formed by the intersection of a cone with a plane that intersects the base of the cone and is not tangent to the cone. The function y(x) = 1/x draws a hyperbola. Category:en:Curves Category:en:Functions

#### Hyperbolic➦

Of or relating to a hyperbolic function
Hyperbolic cosine.

#### Hyperbola➦

A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.

#### Hyperbolic➦

Of or relating to hyperbole.

#### Hyperbola➦

An open curve formed by a plane that cuts the base of a right circular cone

#### Hyperbolic➦

Using hyperbole: exaggerated.

#### Hyperbolic➦

Having a saturation exceeding 100%.

#### Hyperbolic➦

Of or pertaining to a hyperbola.

#### Hyperbolic➦

Indicates that the specified function is a hyperbolic function rather than a trigonometric function.
The hyperbolic cosine of zero is one.

#### Hyperbolic➦

Having negative curvature or sectional curvature.

#### Hyperbolic➦

Whose domain has two (possibly ideal) fixed points joined by a line mapped to itself by translation.

#### Hyperbolic➦

(topology) Of, pertaining to, or in a hyperbolic space a space having negative curvature or sectional curvature.

#### Hyperbolic➦

Belonging to the hyperbola; having the nature of the hyperbola.

#### Hyperbolic➦

Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression.

#### Hyperbolic➦

Enlarged beyond truth or reasonableness;
Had an exaggerated (or inflated) opinion of himself
A hyperbolic style

#### Hyperbolic➦

Of or relating to a hyperbola;
Hyperbolic functions