conic sections - definizione. Che cos'è conic sections
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Cosa (chi) è conic sections - definizione

PLANE CURVE: SYMMETRICAL CONIC SECTION
X squared; Parabolas; Parabolic Equation; Conic section/Proofs; Derivations of Conic Sections; Parabola/Proofs; Derivation of parabolic form; Derivations of conic sections; Parabolic curve; Lambert's Theorem; Parabolae; Parabolic motion
  • Angle trisection with a parabola
  • Parabola (magenta) and line (lower light blue) including a chord (blue). The area enclosed between them is in pink. The chord itself ends at the points where the line intersects the parabola.
  • The parabola is a member of the family of [[conic section]]s.
  • Pencil of conics with a common vertex
  • Pencil of conics with a common focus
  • Parabolic compass designed by [[Leonardo da Vinci]]
  • Parabola: general position
  • Parabola as an affine image of the unit parabola
  • Construction of the axis direction
  • Dual parabola and Bezier curve of degree 2 (right: curve point and division points <math>Q_0, Q_1</math> for parameter <math>t = 0.4</math>)
  • ''p''}} is the ''semi-latus rectum''
  • Perpendicular tangents intersect on the directrix
  • 4-points property of a parabola
  • Parabola: pole–polar relation
  • Midpoints of parallel chords
  • Inscribed angles of a parabola
  • When the parabola <math>\color{blue}{y = 2x^2}</math> is uniformly scaled by factor 2, the result is the parabola <math>\color{red}{y = x^2}</math>
  • Steiner generation of a parabola
  • 2-points–2-tangents property
  • 3-points–1-tangent property
  • Reflective property of a parabola
  • Parabolas <math>y = ax^2</math>
  • Perpendicular from focus to tangent
  • Parabola: pin string construction
  • 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.
  • Parabola and tangent
  • Simpson's rule: the graph of a function is replaced by an arc of a parabola

conic section         
CURVE OBTAINED BY INTERSECTING A CONE AND A PLANE
Conic sections; Conic; Conics; Latus rectum; Conic Sections; Quadratic curve; Conic Sections in Polar Coordinates; Semilatus rectum; Semilatus Rectum; Semi-latus rectum; Conics intersection; Focal parameter; Focal Parameter; Conic Section; Latus Rectum; Dual conic; Directrix (conic section); Directrix of a conic section; Quadratic plane curve; Conic equation; Conic parameter
¦ noun the figure of a circle, ellipse, parabola, or hyperbola formed by the intersection of a plane and a circular cone.
Conic section         
CURVE OBTAINED BY INTERSECTING A CONE AND A PLANE
Conic sections; Conic; Conics; Latus rectum; Conic Sections; Quadratic curve; Conic Sections in Polar Coordinates; Semilatus rectum; Semilatus Rectum; Semi-latus rectum; Conics intersection; Focal parameter; Focal Parameter; Conic Section; Latus Rectum; Dual conic; Directrix (conic section); Directrix of a conic section; Quadratic plane curve; Conic equation; Conic parameter
In mathematics, a conic section (or simply conic, sometimes called a quadratic curve) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though historically it was sometimes called a fourth type.
CONIC         
CURVE OBTAINED BY INTERSECTING A CONE AND A PLANE
Conic sections; Conic; Conics; Latus rectum; Conic Sections; Quadratic curve; Conic Sections in Polar Coordinates; Semilatus rectum; Semilatus Rectum; Semi-latus rectum; Conics intersection; Focal parameter; Focal Parameter; Conic Section; Latus Rectum; Dual conic; Directrix (conic section); Directrix of a conic section; Quadratic plane curve; Conic equation; Conic parameter
["Dynamic Configuration for Distributed Systems", J. Kramer et al, IEEE Trans Soft Eng SE-11(4):424-436 (Apr 1985)].

Wikipedia

Parabola

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.

One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface.

The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola—that is, all parabolas are geometrically similar.

Parabolas have the property that, if they are made of material that reflects light, then light that travels parallel to the axis of symmetry of a parabola and strikes its concave side is reflected to its focus, regardless of where on the parabola the reflection occurs. Conversely, light that originates from a point source at the focus is reflected into a parallel ("collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other waves. This reflective property is the basis of many practical uses of parabolas.

The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic missiles. It is frequently used in physics, engineering, and many other areas.