Eccentricity

Definition

Eccentricity is a parameter associated with conic sections that describes the shape of the curve. It determines how much the conic section deviates from being circular.

5 Must Know Facts For Your Next Test

1. Eccentricity ($e$) is defined as the ratio of the distance from any point on the conic section to its focus and the perpendicular distance from that point to the nearest directrix.
2. For a circle, $e = 0$.
3. For an ellipse, $0 < e < 1$.
4. For a parabola, $e = 1$.
5. For a hyperbola, $e > 1$.

Review Questions

• What is the eccentricity of a circle?
• How does eccentricity differentiate between an ellipse and a hyperbola?
• Calculate the eccentricity of a conic section given its geometric properties.

Related terms

Focus:

A fixed point used in the definition of conic sections.

Directrix:

A fixed line associated with a conic section used in defining its eccentricity.

Conic Sections:

Curves obtained by intersecting a cone with a plane: circles, ellipses, parabolas, and hyperbolas.