Construction of Ellipse by Parallelogram Method

CONSTRUCTION OF ELLIPSE BY PARALLELOGRAM METHOD 

Data known : 

1. Major axis 

2. Minor axis 

3. Angle between major axis and minor axis.

Example 5: Construct an ellipse in a parallelogram with major axis 80mm and minor axis 60mm and angle between major axis and minor axis 60°.

Procedure: 

1. Draw a parallelogram EFGH of size 80mm × 60 mm with an included angle between two sides as 60°.

2. Draw major axis AB bisecting the side EH and minor axis CD, bisecting the side EF. Let the major axis and minor axis intersects at O.

3. Divide the semi minor axis line AH into any number of equal parts (say 4) and name the parts as 1',2′ and 3′ from A.

4. Divide the semi major axis AO into same number of equal parts and name the parts as 1, 2 and 3 from A.

5. Join the points 1', 2' and 3' with C and join the points 1, 2 and 3 with D and extend to intersect the line C-1', C-2' and C-3′ respectively at P1, P2 and P3.

6. Join the points A, P1, P2, P3 and C by a smooth curve which is one-quarter of ellipse.

7. Repeating the same procedure for the remaining three quarters, required ellipse can be obtained oh as shown in Fig. 6.12.