Definition of LOCI:
The word loci is the plural of locus. Loci is a Latin word which is used for location and position. Locus is the set of points that share a similar property or conditions.
Explanation of LOCI:
Let us suppose set of points that are located at the same distance from a specific point say P. All these points collectively form a circular line with P as a point called center of the circle. This can be seen in the figure below
This set of points may be a straight line, line segment, curve or surface whose location can be justified by one or more than one specific similar condition. The circle or Euclidean plane is defined as loci of similar points which are at a given distance from a specific point.
Examples of LOCI:
If we consider a differentiable function the critical loci are defined as the set of critical points of the function. Now if we talk about the algebraic variety the set of singular points is called singular locus or singular loci (plural of locus). If there are two curves which are associated with each other a locus can be defined in the way these curves are associated depending upon the parameter. If we vary the parameter the point of intersection of these curves defines locus.
In the above figure points K and L are the fixed points on a straight line m. Now k is the line drawn variably through the point K. Also the line l drawn through the point L is perpendicular to k. The angle between line k and line m is alpha which the parameter is. Line k and m are commonly associated lines that are dependent on a common parameter. This circle is drawn as locus of the point of intersection of these two associated lines.
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