eccentricity

(noun)

the ratio—constant for any particular conic section—of the distance of a point from the focus to its distance from the directrix

Related Terms

Examples of eccentricity in the following topics:

  • Conic Sections in Polar Coordinates

    • One of the most useful definitions, in that it involves only the plane, is that a conic consists of those points whose distances to some point—called a focus—and some line—called a directrix—are in a fixed ratio, called the eccentricity.
    • The type of a conic corresponds to its eccentricity, those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas.
    • In the focus-directrix definition of a conic, the circle is a limiting case with eccentricity 0.
    • where e is the eccentricity and l is half the latus rectum.

  • Conic Sections

    • There are a number of other geometric definitions possible, one of the most useful being that a conic consists of those points whose distances to some other point (called a focus) and some other line (called a directrix) are in a fixed ratio, called the eccentricity.
    • The type of a conic corresponds to its eccentricity—those with eccentricity less than 1 being ellipses, those with eccentricity equal to 1 being parabolas, and those with eccentricity greater than 1 being hyperbolas.
    • In the focus-directrix definition of a conic, the circle is a limiting case with eccentricity 0.

  • Planetary Motion According to Kepler and Newton

    • The eccentricity of an ellipse tells you how stretched out the ellipse is.
    • The eccentricity can be from 0 to 1.
    • If the eccentricity is equal to zero, that means it is a circle.
    • The eccentricity is what makes an ellipse different from a circle.
    • These values are important because the equation for eccentricity is: