Locus And Basic Locus Cases

locus: it is a path traced out by a point moving in a plane, in a particular manner, for one cycle of operation.

The cases are classified into three categories for easy understanding.

1. Basic locus cases.


2. Oscillating link.


3. Rotating link.

Basic Locus Cases :

Here some geometrical objects like point, line circle will be described with there relative positions. Then one point will be allowed to move in a plane maintaining specific relation with the above objects. And studying the situation carefully you will be asked to draw its locus.

Oscillating & Rotating Link:

Here a link oscillating from one end or rotating around its center will be described. Then a point will be allowed to slide along the link in a specific manner. and now studying the situation carefully you will be asked to draw its locus.

Problems on Locus Part 1

Basic Locus Cases:  

 1 ]  Point F is 50 mm far from a vertical strength line AB. Draw locus of point P, moving in a plane such that it always remains equidistant from point F and line AB.

Solution Steps:

1. locate the center of the line, perpendicular to AB from point F. This will be an initial point P.


2. Mark 5 mm distance to its right side, name those points 1,2,3,4 and from those draw lines parallel to AB.


3. Mark 5 mm distance to its left of P and name it 1.


4. Take F1 distance as radius and F as center draw an arc cutting first parallel line to AB. Name upper point P1 and lower point P2.


5. Similarly repeat this process by taking again 5 mm to right and left and locate P3P4.


6. Join all these points in a smooth curve.


7. It will be the locus of P equidistance from line AB and fixed point F.

 2 ] A circle of 50 mm diameter has it's center 75 mm from a vertical line AB. Draw locus of point P, moving in a plane such that it always remains equidistant from a given circle and line AB.

Solution Steps:

1. locate the center of a line from the periphery of the circle. This will be an initial point P.


2. Mark 5 mm distance to its right side, name those points 1, 2, 3, 4, and from those draw lines parallel to AB.


3. Mark 5 mm distance to its left of p and name it 1, 2, 3, 4.


4. Take c1 distance as radius and C as center draw an arc cutting first parallel line to AB. Name upper point P1 and lower point P2.


5. Similarly repeat this process by taking again 5 mm to right and left and locate P3P4.


6. Join all these points in a smooth curve.


7. It will be the locus of P equidistance from line AB and given circle.

 3 ]  Center of the 30 mm diameter is 90 mm away from the center of the circle of 60 mm diameter. Draw locus of point P, moving in a plane such that it always remains equidistant from given two circles.

Solution Steps:

1. Locate the center of the line, joining two centers but the part in between periphery of two circles. Name it P. this will be initial point p.


2. Mark 5 mm distance to its right side, name those points 1, 2, 3, 4, and from those draw arcs from C1 As center.


3. Mark 5 mm distance to its right side, name those points 1, 2, 3, 4, and from those draw arcs from C2 as a center.


4. Take c1 distance as radius and C as center draw an arc. Name upper point P1 and lower point P2.


5. Similarly repeat this process by taking again 5 mm to right and left and locate P3P4.


6. Join all these points in a smooth curve.


7. It will be the locus of P equidistance from line AB and given circle.

 4 ] In the given situation there are two circles of different diameters and one inclined line AB, as shown.  Draw one circle touching these three objects.

Solution Steps:

1. Here consider two pairs, one is a case of two circles with centers C1 and C2, Draw locus of a point P equidistance from them. ( As per solution of case D above).


2.  Consider the second case that of the fixed circle ( C1 ) and fixed-line AB and draw locus of point P.


3. Locate the point where these two loci interest each other. Name it X, it will be the point equidistance from given two circle and line AB.


4. Take X as a center and it's perpendicular distance on AB as radius, draw a circle which will touch given two circle and line AB.

5 ] Two points A and B are 100 mm apart. There is a point P, moving in a plane such that the difference of its distance from A and B always remains constant and equals to 40 mm. Draw locus of point P.

Solution Steps:

1. Locate A & B points 100 mm apart.


2. Locate point P on AB line, 70 mm from A and 30 mm from B As PA-PB = 40 ( AB = 100 mm )


3. On both sides of the P mark points 5 mm apart. Name those 1, 2, 3, 4, as usual.


4. Now similar to steps of problem 2, Draw different arcs taking A & B centers and A1, B1, A2, B2, etc as the radius.


5. Mark Various positions of p i.e and join them in a smooth possible curve. It will be the locus of P.

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