ellipse

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.