degenerate

(noun)

A conic section which does not fit the standard form of equation.

Related Terms

  • ci
  • center
  • cente
  • Asymptote
  • circle
  • focus
  • eccentricity
  • Parabola
  • ellipse
  • hyperbola
  • asymptote
  • vertex

Examples of degenerate in the following topics:

  • Types of Conic Sections

    • Each shape also has a degenerate form.
    • The degenerate form of the circle occurs when the plane only intersects the very tip of the cone.
    • The degenerate form of an ellipse is a point, or circle of zero radius, just as it was for the circle.
    • The other degenerate case for a hyperbola is to become its two straight-line asymptotes.
    • It also shows one of the degenerate hyperbola cases, the straight black line, corresponding to infinite eccentricity.
  • Nonlinear Systems of Equations and Problem-Solving

    • In modern geometry, certain degenerate cases, such as the union of two lines, are included as conics as well.
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