Construction of Elllipse by Arcs of Circles Method

CONSTRUCTION OF ELLLIPSE BY ARCS OF CIRCLES METHOD 

Data known : 

1. Major axis

2. Distance between Foci

Example 2: Construct an ellipse with major axis 90 mm and the distance between the Foci is 70mm.

Procedure:

1. Draw major axis AB of length 90mm and locate the centre 'O'.

2. Locate Foci F1, F2 on major axis AB, such that OF1 = OF2 = 70/2 = 35mm.

3. Along the major axis AB and in between the Foci points F1 and F2, mark the points 1, 2, 3 .... at approximately equal intervals (need not be equal).

4. With F1 as centre and A-1 as radius draw two arcs on both sides of AB. Again with F2 as centre and B-1 as radius draw two arcs to cut the previous two arcs at P1 and P1'.

5. similarly with F1 as centre A-2 as radius draw two arcs on both sides of AB. Again with F2 as centre and B-2 as radius draw two arcs to cut the previous two arcs at P2 and P2'.

6. Repeating the above steps with F1 and F2 as centres and radii A-3 and B-3 draw the arcs intersecting at P3 and P3'.

7. In the same way locate the other points P4, P4', P5, P5' etc.,

8. Draw a perpendicular passing through centre O.

9. With F1 as centre and O-A as radius draw arcs to cut the perpendicular passing through at C and D. Now, CD represents the minor axis of ellipse.

10. Join all the points A, P1, P2, P3 etc. by a smooth curve and complete the curve, which is the required ellipse.