CONJUGATE FOCI Meaning and
Definition
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Conjugate foci refer to two specific points within an ellipse or a hyperbola that possess a unique mathematical relationship. These foci are two points located inside the curve, usually on the major axis, and they play a crucial role in defining the shape of the curve.
In the case of an ellipse, conjugate foci are two points that lie on the major axis, equidistant from the center of the ellipse. The sum of the distances from any point on the ellipse to these two foci is constant and equal to the length of the major axis. This property is known as the "conjugate property" or the "property of conjugate foci."
Similarly, for a hyperbola, conjugate foci are two points located on the major axis, also equidistant from the center. However, in this case, the difference in distance from any point on the hyperbola to these two foci is constant and equal to the distance between the vertices of the hyperbola.
Conjugate foci have significant geometric and mathematical implications. They help determine the shape, size, and orientation of the ellipse or hyperbola. They also aid in solving various problems and measurements related to these curves, such as determining the eccentricity or finding the equations of the curves.
The concept of conjugate foci is an essential element of conic section geometry and plays a fundamental role in understanding and analyzing ellipses and hyperbolas.
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Two points in relation to two lenses or concave mirrors, so in relation to each other that the rays from a light at one point are focussed at the other, and vice versa.
A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.
Common Misspellings for CONJUGATE FOCI
- conjugate fobi
- conjugate focy
- conjugate foca
- conjugate focm
- conjugate foch
- c onjugate foci
- co njugate foci
- con jugate foci
- conj ugate foci
- conju gate foci
- conjug ate foci
- conjuga te foci
- conjugat e foci
- conjugate f oci
- conjugate fo ci
- conjugate foc i
Etymology of CONJUGATE FOCI
The word "conjugate" comes from the Latin word "conjugare", which means "to join together" or "to unite". It was originally used in mathematics and specifically in terms of joining or combining elements in complex numbers.
"Foci" is the plural form of the Latin word "focus", which means "hearth" or "fireplace". In mathematics and physics, it refers to the points of greatest intensity or concentration in a curve or an ellipse.
When these two words are combined, "conjugate foci" refers to a pair of foci in an ellipse or hyperbola that are symmetrically placed with respect to the center of the curve. The "conjugate" aspect indicates the joining or uniting of these foci within the curve.
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