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jedishrfu

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Placing the thumb tacks in the middle of the paper some small distance apart, say 2 inches and then wrapping the string around both thumb tacks and the pencil to create a triangle. Now move the pencil clockwise around keeping the string taut to create an ellipse. From this you can see that the two thumb tacks control the shape of the ellipse. They are in fact at the foci of the ellipse.

Here's another related way to draw it:

http://www.mathopenref.com/printellipse1.html

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Mark44

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The idea with the string is that you pull it so that it is taut.So you mean that suppose I take the same thumb tacks but I pull the string with a bit lesser force. Now I pull the string till as much as it can stretch. Now in the first case if the sum of distances of all the points is 12. In the latter case when i pull the string hard also the sum of all the distances will be 12. Am I right? But for a point that is not the focus the sum of distances will vary when the shape changes. Am I right?

Here is a picture of what jedishrfu is talking about. The foci (plural of focus) are at F

If you move one or both of the thumbtacks, which changes the location of the foci, you get a different ellipse.

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Mark44

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jedishrfu

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Thanks a lot. That is as simple as it can get. I get the point.The idea with the string is that you pull it so that it is taut.

Here is a picture of what jedishrfu is talking about. The foci (plural of focus) are at F1and F2 and P is an arbitrary point on the ellipse. For an ellipse, the sum of the lengths of the segments F1P and PF2 is a constant. As we move around the ellipse to the right, the segment F1P gets longer and the segement PF2 gets shorter, but the sum F1P + PF2 remains the same.

If you move one or both of the thumbtacks, which changes the location of the foci, you get a different ellipse.

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