ellipse

(noun)

a closed curve; the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone

Related Terms

  • gravitational constant
  • eccentricity

Examples of ellipse in the following topics:

  • Planetary Motion According to Kepler and Newton

    • Kepler explained that the planets move in an ellipse around the Sun, which is at one of the two foci of the ellipse.
    • The eccentricity of an ellipse tells you how stretched out the ellipse is.
    • The eccentricity is what makes an ellipse different from a circle.
    • Therefore, the period ($P$) of the ellipse satisfies:
    • The important components of an ellipse are as follows: semi-major axis $a$, semi-minor axis $b$, semi-latus rectum $p$, the center of the ellipse, and its two foci marked by large dots.
  • Conic Sections in Polar Coordinates

    • Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse.
    • The circle is a special case of the ellipse, and is of such sufficient interest in its own right that it is sometimes called the fourth type of conic section.
    • 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.
    • As in the figure, for $e = 0$, we have a circle, for $0 < e < 1$ we obtain an ellipse, for $e = 1$ a parabola, and for $e > 1$ a hyperbola.
  • Conic Sections

    • Traditionally, the three types of conic section are the hyperbola, the parabola, and the ellipse.
    • The circle is a special case of the ellipse, and is of such interest in its own right that it is sometimes called the fourth type of conic section.
    • 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.
    • If they are bound together, they will both trace out ellipses; if they are moving apart, they will both follow parabolas or hyperbolas.
    • Ellipse; 3.
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