Definition

1. Noun:
   • A specific type of plane curve: A parabola is a symmetrical open curve formed by the intersection of a cone with a plane parallel to its side. It is the set of all points in a plane that are equidistant from a fixed point (the focus) and a fixed straight line (the directrix).

Examples of Usage

• Noun:
  • The path of a thrown ball approximates a parabola.
  • The satellite dish has a parabolic shape, which is a three-dimensional form based on a parabola.
  • In algebra, the graph of the equation y = x² is a simple parabola.

Advanced Usage

• "Parabolic" (Adjective): Describing something that has the shape of or relates to a parabola.
  • The bridge's parabolic arch is both strong and elegant.
• In Physics: The term is used to describe a projectile's trajectory under uniform gravity, ignoring air resistance.
  • The cannonball followed a nearly parabolic arc.

Variants and Related Words

• Parabolic (adj): Having the form of or relating to a parabola.
• Paraboloid (n): A surface generated by rotating a parabola around its axis.
• Paraboloidal (adj): Relating to or shaped like a paraboloid.

Synonyms

• Conic section: A parabola is one of the four types of conic sections (along with the circle, ellipse, and hyperbola).
• Quadratic curve: A curve represented by a second-degree polynomial equation.

Related Phrases and Idioms

(This word is a specific technical term and is not commonly used in idiomatic expressions or phrasal verbs.)

Noun

1. a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve