Question

What is locus?

Answer 1

Remember:
A locus is just a set of points.

Explanation:

Locus is an important concept in co-ordinate geometry

So understand this concept well and your god to go;

Lets understand this concept with an example of a cow;

A cow is tethered to a post with a rope of length 4m. It walks around the post with the rope pulled tight.

The cow's path is a circle of radius 4m.

The cow's path is known as the locus.

The plural of locus is loci.

Now lets generalize this;

A locus is a set of points which satisfies a certain condition.

In the above example the cow satisfies the condition of being 4 m away from an absolute point so it is a locus.

Another example is ripples in water

Let go deeper;

There are 5 Theorems pertaining to loci;

Locus Theorem 1:

The locus of points at a fixed distance, d, from point P is a circle with the given point P as its center and d as its radius.(This is the cow example)

Locus Theorem 2:

The locus of points at a fixed distance, d, from a line, l, is a pair of parallel lines d distance from l and on either side of l.

Locus Theorem 3:

The locus of points equidistant from two points is the perpendicular bisector of the line segment determined by the two points.

Locus Theorem 4:

The locus of points equidistant from two parallel lines

Locus Theorem 5:

The locus of points equidistant from two intersecting lines

That should be a good start for coordinate geometry