In mathematics

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...

, the eccentricity, denoted e or , is a parameter

Parameter

Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....

 associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.

In particular,

• The eccentricity of a circle
  Circle
  A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
  
   is zero.
• The eccentricity of an ellipse
  Ellipse
  In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
  
   which is not a circle is greater than zero but less than 1.
• The eccentricity of a parabola
  Parabola
  In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface...
  
   is 1.
• The eccentricity of a hyperbola
  Hyperbola
  In mathematics a hyperbola is a curve, specifically a smooth 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 components or branches, which are mirror...
  
   is greater than 1.

Furthermore, two conic sections are similar

Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape. More precisely, either one is congruent to the result of a uniform scaling of the other...

 if and only if they have the same eccentricity.
Any conic section can be defined as the locus of points whose distances are in a constant ratio to a point (the focus) and a line (the directrix).