Math 2.0

Geometry Definition

Eccentricity

Builds on Conic sectionFocus of a conicDirectrix

Definition

Let QQ be a non-degenerate conic section in the Euclidean plane ℝ2\mathbb{R}^2. If QQ is a circle, its eccentricity is e=0e = 0. Otherwise, let FF be a focus of QQ and ℓ\ell the directrix for FF. The eccentricity of QQ is the constant ratio e=d(P,F)d(P,ℓ),P∈Q.e = \frac{d(P, F)}{d(P, \ell)}, \qquad P \in Q.

Remarks

An ellipse has 0≤e<10 \leq e < 1, a parabola has e=1e = 1 and a hyperbola has e>1e > 1. For an ellipse or a hyperbola with the semi-major axis aa and the foci at the distance cc from the centre, e=c/ae = c / a. Two conic sections with the same eccentricity are similar.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

Show the path as a graph
Conic section, concept, no evidence levelConic sectionconceptDirectrix, concept, no evidence levelDirectrixconceptFocus of a conic, concept, no evidence levelFocus of a conicconceptEccentricity, definition, no evidence levelEccentricitydefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Conic section concept
  2. Directrix concept
  3. Focus of a conic concept
  4. Eccentricity definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Eccentricity_(mathematics), Definitions
  2. Web https://en.wikipedia.org/wiki/Eccentricity_(mathematics), Values
About this page
Tag0GCWJS2EGB
URIm2://0GCWJS2EGB
Kinddefinition
WritingW1 stated
MSC51N20
DefinesEccentricity
UsesConic section, Focus of a conic, Directrix

Markdown · JSON · Edit on GitHub

What this page needs for W2

  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

No page links to this page yet.