Math՚s: Lines and Angles: Locus of a Point under Some of the Conditions (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 Meaning

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.

Locus of Point under Some Conditions

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.

Locus of Point
  • 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 .
Bisector of the Line Segment
  • 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 .
Locus of a Point Equidistant

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