conic section

Thân thiện

A student draws a conic section on the chalkboard.

Definition

1. Noun:
   • (Geometry) A curve generated by the intersection of a plane and a circular cone: A "conic section" is a curve obtained by slicing a double-napped right circular cone with a plane. The specific shape of the curve depends on the angle at which the plane intersects the cone.

Examples of Usage

• Noun:
  • The circle, ellipse, parabola, and hyperbola are all types of conic section.
  • Studying the properties of a conic section is fundamental in analytic geometry.

Advanced Usage

• "Degenerate conic section": A conic section that is a point, a line, or a pair of intersecting lines, formed when the slicing plane passes through the vertex of the cone.
  • When the plane cuts through the apex, the resulting conic section is degenerate.

Variants and Related Words

• Conic (noun/adjective): Often used as a shorter form for "conic section" or to describe something related to a cone.
  • The orbit of a planet is a conic with the sun at one focus.

Synonyms

• Conic: A common synonym, especially in mathematical contexts.
• Quadratic curve: Refers to the fact that all non-degenerate conic sections can be represented by a second-degree (quadratic) equation in two variables.

Related Phrases

• Conic section geometry: The branch of geometry dealing with these curves.
• Focus of a conic section: A fixed point used in the geometric definition of ellipses and hyperbolas.

Related Idioms

(This term is highly technical and does not have common idiomatic expressions.)

Học thuật

Noun

1. (geometry) a curve generated by the intersection of a plane and a circular cone

Từ đồng nghĩa

• conic