In mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 a hyperbola is a curve, specifically a smooth
Smooth function
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...

 curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected component
Connected component (graph theory)
In graph theory, a connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices. For example, the graph shown in the illustration on the right has three connected components...

s or branches, which are mirror images of each other and resembling two infinite bows
Bow (weapon)
The bow and arrow is a projectile weapon system that predates recorded history and is common to most cultures.-Description:A bow is a flexible arc that shoots aerodynamic projectiles by means of elastic energy. Essentially, the bow is a form of spring powered by a string or cord...

. The hyperbola is one of the four kinds of conic section
Conic section
In mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...

, formed by the intersection of a plane
Plane (mathematics)
In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...

 and a cone
Cone (geometry)
A cone is an n-dimensional geometric shape that tapers smoothly from a base to a point called the apex or vertex. Formally, it is the solid figure formed by the locus of all straight line segments that join the apex to the base...