Locus (mathematics)

In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets.

[3] In contrast to the set-theoretic view, the old formulation avoids considering infinite collections, as avoiding the actual infinite was an important philosophical position of earlier mathematicians.

[4][5] Once set theory became the universal basis over which the whole mathematics is built,[6] the term of locus became rather old-fashioned.

A triangle ABC has a fixed side [AB] with length c. Determine the locus of the third vertex C such that the medians from A and C are orthogonal.

If the parameter varies, the intersection points of the associated curves describe the locus.

For example,[1] the locus of the inequality 2x + 3y – 6 < 0 is the portion of the plane that is below the line of equation 2x + 3y – 6 = 0.

Each curve in this example is a locus defined as the conchoid of the point P and the line l . In this example, P is 8 cm from l .
(distance PA ) = 3.(distance PB )
Locus of point C
The locus is a circle
The intersection point of the associated lines k and l describes the circle