Locus

In Geometry, a locus is a set of points whose location satisfies or is determined by one or more specified conditions i.e., 1)every point satisfies a given condition and 2)every point satisfiying it is in that particular locus.

• The set of points equidistant from two points is a perpendicular bisector to the line segment connecting the two points.

• The set of points equidistant from two lines which cross is the angle bisector.

• All conic sections are loci:
• Parabola: the set of points equidistant from a single point (the focus) and a line (the directrix).
• Circle: the set of points for which the distance from a single point is constant (the radius). The set of points for each of which the ratio of the distances to two given foci is a positive constant (that is not 1) is referred to as a Circle of Apollonius.
• Hyperbola: the set of points for each of which the absolute value of the difference between the distances to two given foci is a constant.
• Ellipse: the set of points for each of which the sum of the distances to two given foci is a constant. In particular, the circle is a locus.