Construction of Ellipse by Concentric Circles Method

CONSTRUCTION OF ELLIPSE BY CONCENTRIC CIRCLES METHOD 

Data known :

1. Major axis 

2. Minor axis

Example 3: Construct an ellipse with major axis 100mm and minor axis 80mm by concentric circles method.

Procedure:

1. Draw major axis AB of length 100mm and minor axis CD of length 80mm, perpendicular to AB and passing through its mid point O.

2. With O as centre and radii equal to half of the major and minor axes. (ie., OA and OC respectively) draw concentric circles.

3. Divide the major axis circle into 12 equal parts (at an interval of 30°) and mark the points on circumference as 1, 2, 3 etc.,

4. Draw lines joining these points with O, intersecting the minor axis circle at 1',2',3' etc.,

5. Through the point 1 draw a vertical line parallel to CD and through the point 1' draw a horizontal line parallel to AB, intersecting each other at P1.

6. Similarly draw vertical lines through 2, 3, 4 etc., and horizontal lines through 2',3',4' etc., intersecting at P2, P3, P4 etc.,

7. Join the points A, P1, P2,.....A by a smooth curve by free hand