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# Junior Inter Mathematics LOCUS Practice Paper

Definition: The set of all points (and only those points) which satisfy the given geometrical condition(s) (or properties) is called a locus.

Eg. The set of points in a plane that are at a constant distance r from a given point C is a locus.
Here the locus is a circle.

2. The set of points in a plane that are equidistant from two given points A and B is a locus. Here the locus is a straight line and it is the perpendicular bisector of the line segment joining A and B.

EQUATION OF A LOCUS :
An equation f(x, y) = 0 is said to be the equation of a locus S if every point of S satisfies f(x, y) = 0 and every point that satisfies f(x, y) = 0 belongs to S.

An equation of a locus is an algebraic description of the locus. This can be obtained in the following way
(i) Consider a point P(x, y) on the locus

(ii) Write the geometric condition(s) to be satisfied by P in terms of an equation or in the equation in symbols.

(iii) Apply the proper formula of coordinate geometry and translate the geometric condition(s) into an algebraic equation.

(iv) Simplify the equation so that it is free from radicals. The equation thus obtained is the required equation of locus.