Conic Section

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The conic sections are the classes of nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. A conic section can also be realized as the zero set of a quadratic equation in two variables.

Conic section is a high school-level concept that would be first encountered in a pre-calculus course covering conic sections. It is listed in the California State Standards for Mathematical Analysis.


Circle: A circle is the set of points in a plane that are equidistant from a given center point.
Ellipse: A conic section with eccentricity less than one. It resembles a squashed circle.
Hyperbola: A hyperbola is a conic section with eccentricity greater than one and consists of two separate branches.
Parabola: A parabola is a conic section with eccentricity equal to one. Parabolas appear as the graphs of quadratic equations and the trajectories of projectiles.


Cone: A cone is a pyramid with a circular cross section.
Cross Section: The cross section of a solid is a plane figure obtained by the intersection of that solid with a plane.
Curve: A curve is a continuous map from a one-dimensional space to an n-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve.

Classroom Articles on Conic Sections

  • Locus

  • Classroom Articles on Pre-Calculus (Up to High School Level)

  • Asymptote
  • Normal Vector
  • Complex Conjugate
  • Parametric Equations
  • Complex Number
  • Plane
  • Complex Plane
  • Plane Curve
  • Cross Product
  • Polar Coordinates
  • Determinant
  • Range
  • Domain
  • Rational Function
  • Dot Product
  • Reflection
  • e
  • Rotation
  • Exponential Function
  • Rotation Matrix
  • Function
  • Scalar
  • i
  • Spherical Coordinates
  • Imaginary Number
  • Tangent Line
  • Inverse Function
  • Translation
  • Logarithm
  • Vector
  • Natural Logarithm