Eccentricity

Eccentricity: how much a conic section (a circle, ellipse, parabola or hyperbola)
varies from being circular.

A circle has an eccentricity of zero, so the eccentricity shows you how "un-circular" the curve is. Bigger eccentricities are less curved.

Different values of eccentricity make different curves:

  • At eccentricity = 0 we get a circle
  • for 0 < eccentricity < 1 we get an ellipse
  • for eccentricity = 1 we get a parabola
  • for eccentricity > 1 we get a hyperbola
  • for infinite eccentricity we get a line

Eccentricity is often shown as the letter e (don't confuse this with Euler's number "e", they are totally different)

Eccentricity

Animation

Try the slider under the graph to see what happens:


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Calculating The Value

circle For a circle, eccentricity is 0
ellipse on xy graph

For an ellipse, eccentricity is:

ellipse eccentricity

parabola For a parabola, eccentricity is 1
hyperbola on xy graph

For a hyperbola, eccentricity is:

hyperbola eccentricity