parabola

thumb|right|upright=1.36|Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward. thumb|The parabola is a member of the family of conic sections.

AI overview

A parabola is a curved shape that you get when you slice through a cone at a certain angle, and it's one of the fundamental curves studied in mathematics because it appears throughout nature and engineering. The curve extends infinitely in certain directions and has special mathematical properties that make it useful for applications like satellite dishes and projectile paths.

AI-generated from the Wikipedia summary — may contain errors.

Described at

Parabolas: Definitions, Equations, and Practical Example - Andrea Minini

andreaminini.net →

A parabola is a second-order plane algebraic curve, defined as the set of all points equidistant from a fixed point called the focus (F) and a fixed line (d) called the directrix , which does not pass through the focus. In other words, the points on the parabola form a geometric locus because they are equidistant from the focus (F) and the directrix (d) of the parabola. The axis of the parabola is the line that passes through the focus and is perpendicular to the directrix. The vertex of the parabola is the point where the axis intersects the parabola. This indicates that in a parabolic mirror, any ray parallel to the focal axis is reflected directly towards the focal point (F). As a result, all rays parallel to the focal axis converge at a single point. This principle is the basis for satellite dish antennas and concentrated solar power panels. Conversely, if the focal point (F) is a light source, all the rays reflected by the parabolic mirror will run parallel to the focal axis.

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Wikidata facts

Image: Parabola3.svg

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Commons category: Parabolas
described at URL: testbook.com/maths/parabola

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Article

63 sections

Contents

History
Definition as a locus of points
In a Cartesian coordinate system
Axis of symmetry parallel to the ''y'' axis
General position
As a graph of a function
Similarity to the unit parabola
As a special conic section
In polar coordinates
Conic section and quadratic form
Diagram, description, and definitions
Derivation of quadratic equation
Focal length
Position of the focus
Alternative proof with Dandelin spheres
Proof of the reflective property
Construction and definitions
Deductions
Other consequences
Tangent bisection property
Intersection of a tangent and perpendicular from focus
Reflection of light striking the convex side
Alternative proofs
Pin and string construction
Properties related to Pascal's theorem
4-points property
3-points–1-tangent property
2-points–2-tangents property
Axis direction
Steiner generation
Parabola
Dual parabola
Inscribed angles and the 3-point form
Pole–polar relation
Tangent properties
Two tangent properties related to the latus rectum
Orthoptic property
Lambert's theorem
Facts related to chords and arcs {{anchor|Chords|Arcs}}
Focal length calculated from parameters of a chord
Area enclosed between a parabola and a chord
Corollary concerning midpoints and endpoints of chords
Arc length
A geometrical construction to find a sector area
Focal length and radius of curvature at the vertex
As the affine image of the unit parabola
Parametric representation
Vertex
Focal length and focus
Implicit representation
Parabola in space
As quadratic Bézier curve
Numerical integration
As plane section of quadric
As trisectrix
Generalizations
In the physical world
Gallery
See also
Footnotes
References
Further reading
External links

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.