CONIC SECTIONS Meaning and
Definition
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Conic sections refer to a set of curves formed by intersecting a cone with a plane. These curves include the circle, ellipse, parabola, and hyperbola. Conic sections have been studied since ancient Greece and have significant applications in various fields, including physics, engineering, mathematics, and astronomy.
A circle is a conic section with an eccentricity of zero, formed by intersecting a cone with a plane that is perpendicular to the cone's axis. It is defined by a set of points equidistant from a fixed point called the center.
An ellipse is a conic section with an eccentricity between 0 and 1, formed by intersecting a cone with a plane that is inclined to the cone's axis. It is defined by a set of points that have a constant sum of distances from two fixed points called the foci.
A parabola is a conic section with an eccentricity of one, formed by intersecting a cone with a plane parallel to one of the cone's sides. It is defined by a set of points equidistant from a fixed point called the focus and a fixed line called the directrix.
A hyperbola is a conic section with an eccentricity greater than 1, formed by intersecting a cone with a plane that is further inclined to the cone's axis. It is defined by a set of points that have a constant difference in distances from two fixed points called the foci.
In summary, conic sections represent a family of curves obtained by intersecting a cone with a plane, including circles, ellipses, parabolas, and hyperbolas. Each type has distinct geometric properties and is important in various mathematical and scientific fields.
Etymology of CONIC SECTIONS
The word "conic sections" comes from the combination of two different origins: "conic" and "sections".
1. "Conic" is derived from the Greek word "konikos", which means "related to a cone". It is formed by the noun "konos", meaning "cone". The Greek mathematician Apollonius of Perga extensively studied curves formed by intersecting a plane with a right circular cone, and these curves became known as conic sections. The adjective form "conic" is used to describe things related to or derived from cones.
2. "Sections" is derived from the Latin word "sectio", which means "a cutting". It originates from the verb "secare", meaning "to cut". In mathematics, "section" refers to the act of cutting or dividing an object into parts or portions.
