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What Are Loci in Geometry?


A locus is a set of points that satisfies a specified condition. Here are some loci you need to know:

Theory

Loci

Circle:

All points on a circle have the same distance from its center point.

Ellipse:

The sum of the distances to the two focal points is the same for all points on the ellipse.

Equidistant Line:

All points that are equidistant from two specified points.

Parallels:

All points equidistant to a specified straight line.

Bisector:

All points equidistant to two specified lines.

Circle of Apollonius:

Every angle v that spans a line segment. Added together, these angles create a circle.

On exams, you may be asked what locus is being described. For that reason, it will be useful to remember what defines the different loci.

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