# Math's: Lines and Angles: Locus of a Point under Some of the Conditions

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## Locus- Meaning

Locus is a figure that shows the path traced by a point (or a very small particle) moving under certain conditions.

For example, in the game of cricket, when a player hits the ball, it describes a path, before being caught or touching the ground. The path described will be known as Locus.

## Locus of a Point under Some of the Conditions

Given two parallel lines and , also a particle between them equidistant from both the lines. If the particle moves so that it is equidistant from both the lines, then the path traced by will be a line parallel to both the lines and exactly in the middle of them as shown in the following figure.

Given a fixed point and a point at a fixed distance . If the point moves in a plane so that it is always at a constant distance from the fixed point , then the path of the moving point will be a circle as shown in the following figure.

The locus of a point equidistant from two given points is the perpendicular bisector of the line segment joining the two points.

Thus, if we have two given points and and we have to find the locus of a point such that , then the locus of will be divides into two equal parts . Also . That is is perpendicular bisector of .

The locus of a point equidistant from two intersecting lines is the pair of lines, bisecting the angles formed by the given lines.

Thus, if we have two lines and intersecting at and we have to find the locus of a point which is equidistant from both and .

If we take any point P on any of or (bisector of & that of respectively, we will find perpendicular distances and PM of from the lines and are equal. That is,

If we take any other point, say , not lying on any bisector or , then will not be equal to .