Page 79 - Mathematics Class - XI

6. Join the points A to points, A , A , A , ... and draw the lines joining the point D to B , B , B , ... .
1 2 3 1 2 3
7. Mark the point of intersection of AA and DB as S , AA and DB as S , AA and DB as S and so on.
1 1 1 2 2 2 3 3 3
8. Fix nails at the points S , S , S , ... S .
10
3
1
2
9. Join the feet of nails with thread/wires.
10. Repeat the same activity for remaining three congruent rectangles and obtain the curve as shown in
Fig. (a).

DEMONSTRATION

1. The curve so obtained is an ellipse.
2. The major axis of this ellipse is the length of the rectangle PQRS.

3. The minor axis of this ellipse is the breadth of the rectangle PQRS.

OBSERVATION
By actual measurement,

1. Length of the rectangle PQRS = ___________

2. Breadth of the rectangle PQRS = ___________
3. Major axis of the ellipse = ___________

4. Minor axis of the ellipse = ___________

CONCLUSION
This activity shows that we can construct an ellipse using a given rectangle.

APPLICATION
This activity is helpful in understanding the concept such as major and minor axes of an ellipse. It is also useful
in drawing elliptical designs such as swimming pools, tables, etc.

Knowledge Booster

Latus rectum of an ellipse is a line
segment perpendicular to the major axis
through any of the foci (F or F ) and
1
2
whose end points lie on the ellipse.

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