Page 82 - Mathematics Class - XI

DEMONSTRATION

1. Fix the two ends of the string of length 14 cm at the two nails at F and F .
1 2
2. With a pencil, stretch the string in the loop without slack and mark at least 10 points A , A , A , ..., etc., on
3
2
1
both sides of the line segment joining F and F .
1 2
3. Join all the points A , i = 1, 2, ... 20 to form an ellipse.
i
OBSERVATION

1. A F + A F = 14 cm
1 1 1 2

2. A F + A F = 14 cm
2 1
2 2
3. A F + A F = 14 cm
3 1 3 2

4. A F + A F = 14 cm
4 2
4 1
5. A F + A F = 14 cm
6 1 6 2
6. A F + A F = 14 cm
9 1 9 2
7. A F + A F = A F + A F = A F + A F
4 2
4 1
19 2
19 1
3 1
3 2
8. We observe that, sum of the distances of each of the points A , A , A ,... from the points F and F is equal,
3
2
2
1
1
i.e., constant. So, the curve obtained is an ellipse.
CONCLUSION
We can construct an ellipse when two fixed point are given.
APPLICATION
This activity can be used to explain the property of an ellipse , i.e., the sum of the distances of any point on the
ellipse from its two foci is constant and is equal to length of major axis.

Knowledge Booster
The sum of distances of a point on the ellipse from the
two fixed points (Foci) is always greater than the distance
between two fixed points (Foci).

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