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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.**

**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.*