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Activity 7 Class Xi

1. To construct an ellipse, two fixed points F and F2 are chosen on a paper sheet. 2. A string longer than the distance between F and F2 (e.g. 9 cm) is tied to one end at F and the other end at F2. 3. By moving a pencil around the loop of string while keeping it taut, an elliptical curve is drawn on the sheet whose every point satisfies the property that its distance from F plus its distance from F2 equals the string length.

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Annanya Verma
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678 views1 page

Activity 7 Class Xi

1. To construct an ellipse, two fixed points F and F2 are chosen on a paper sheet. 2. A string longer than the distance between F and F2 (e.g. 9 cm) is tied to one end at F and the other end at F2. 3. By moving a pencil around the loop of string while keeping it taut, an elliptical curve is drawn on the sheet whose every point satisfies the property that its distance from F plus its distance from F2 equals the string length.

Uploaded by

Annanya Verma
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Ohjective

ODIonstruct ct an ellipse when two fixed


To. points are
given.
Method ofConstruction
M e t

1.
Take a drawing board and fix the white
sheet on it with board pins.
Take two points F and F2 on the paper
2. Take two
white
Material Required
FF 6 cm and then join F^ and F. paper sheet such that A drawing board
Fix two nails at F and F. A white paper sheet
3.
4. Take a string whose length is more than Board pins
Tie one end of the string with F,F, or 6 cm. Let it be 9 cm. Nails, string, pen, etc.
F and other end at F.

P2 P
X X Note: Construct another ellipse
by taking different length of the
P string and also by changing the
P10 Pg distance between F and F2.

Demonstration
1. Take a pencil and stretch the string in the loop without slack. Now move the pencil all around F,F2 in
such a way that string is fully stretched without any slack. The pencil will draw a curve on the white
paper sheet as shown in figure. It is an ellipse.
2. Now take some points, P, P2, Pa, Pa, Ps, Po, P7, Pa, Po, P1o and Pi1 on the curve.

Observation
1. PF + P,F2 9 cm.
2. PaF + P2F2 = 9 cm.
3 .P F , + P F , = 9 cm, PAF1 + P,F2 = 9 cm, PsF1 + PsF2 9 cm, PgF1 + PgF2 = 9 cm, so on, we get

PgF+PgF =
9 cm.
4. Sum of the distances of each of the points Pi, P2, P3 . from the points F and F, is 9 cm.

5. So the curve obtained is an ellipse.

Application
his activity is used to explain the concept of an ellipse. It explains that the sum of the distances of a point on
he curve from two fixed point is same, i.e, if P is any general point on the ellipse then PF, + PF, = a constant.

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