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Straight Lines

Locus and Its Equation

Let us look at the following figure.

This is a circle with centre at O; and P, Q and R are points on it.
Now, the question arises − what is a circle?
A circle is a set of points, which are equidistant from a fixed point. The fixed point is called the centre and the fixed distance is called the radius of the circle.
Does the circle satisfy any geometrical condition?
Yes, it does. The geometrical condition is that “the set of all points are equidistant from a fixed point”. Such geometrical condition satisfied by a circle for all points on it is called locus.
Therefore, locus can be defined as:

The locus is the set of all those points, which satisfy the given geometrical condition(s).

Or

The locus of a point is the path traced out by the point moving under given geometrical condition(s).

Clearly, circle is a locus of a point equidistant from a fixed point.
Similarly, we can define a parallel line to a fixed line as “the locus of point equidistant from a fixed line” as shown below:


Equation of a Locus

An equation is said to be the equation of locus of a moving point if :

  • the coordinates of every point on the locus satisfy the equation

  • the coordinates of any point satisfy the equation, then the point must lieā€¦

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