Introduction to locus :
The word loci is the plural of the word locus. This is a Latin word meaning "place". Though it has several meanings let us discuss the mathematical meaning of locus or loci in this article. In mathematics, locus is the set of points satisfying a particular condition forming a geometrical figure. Let us discuss locus in detail.
Definition of locus
Locus of a point is the path traced by the point which moves under certain geometrical conditions. More precisely, locus is the set f all points which satisfy a given geometrical conditions or conditions.
Locus - Loci - Examples
The set of all points in a plane such that the distance of each point from a fixed point in the plane is a constant is a locus. We know that this locus is a circle whose centre is the fixed point and whose radius is the constant distance.
Consider the locus of a point which moves so that it is equidistant from two given points A and B. It is the perpendicular bisector of the line AB.
Consider two lines AOB and COD intersecting at O. A point moves so that it is equidistant from those of the two lines. Clearly the path traced by the point is either the internal or external bisector of the angle between AOB , COD. So, here the locus consists of two straight lines bisecting the angles between the lines AOB , COD.
How to Find the Equation of a Locus ( Loci)
Any geometrical condition satisfied by a point ( a , b ) on a locus can be expressed algebraically as a relation between a and b. The relation thus obtained is called the equation of the locus. To find the equation of a locus, we take a point ( a , b ) on the locus and use the given conditions to obtain the relation between a and b . The equation of the locus thus obtained is satisfied by the co-ordinates of every point on the locus and by the coordinates of no other point.
The word loci is the plural of the word locus. This is a Latin word meaning "place". Though it has several meanings let us discuss the mathematical meaning of locus or loci in this article. In mathematics, locus is the set of points satisfying a particular condition forming a geometrical figure. Let us discuss locus in detail.
Definition of locus
Locus of a point is the path traced by the point which moves under certain geometrical conditions. More precisely, locus is the set f all points which satisfy a given geometrical conditions or conditions.
Locus - Loci - Examples
The set of all points in a plane such that the distance of each point from a fixed point in the plane is a constant is a locus. We know that this locus is a circle whose centre is the fixed point and whose radius is the constant distance.
Consider the locus of a point which moves so that it is equidistant from two given points A and B. It is the perpendicular bisector of the line AB.
Consider two lines AOB and COD intersecting at O. A point moves so that it is equidistant from those of the two lines. Clearly the path traced by the point is either the internal or external bisector of the angle between AOB , COD. So, here the locus consists of two straight lines bisecting the angles between the lines AOB , COD.
How to Find the Equation of a Locus ( Loci)
Any geometrical condition satisfied by a point ( a , b ) on a locus can be expressed algebraically as a relation between a and b. The relation thus obtained is called the equation of the locus. To find the equation of a locus, we take a point ( a , b ) on the locus and use the given conditions to obtain the relation between a and b . The equation of the locus thus obtained is satisfied by the co-ordinates of every point on the locus and by the coordinates of no other point.
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