- #1
The idea with the string is that you pull it so that it is taut.avito009 said: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?
Mark44 said: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.
The foci of an ellipse are two fixed points located inside the ellipse, each at a distance from the center of the ellipse. These points determine the shape and size of the ellipse.
The foci of an ellipse can be calculated using the formula c = √(a² - b²), where a is the length of the semi-major axis and b is the length of the semi-minor axis.
The foci in an ellipse play a crucial role in determining the eccentricity of the ellipse, which is a measure of how elongated the ellipse is. They also help in defining the directrix, which is a line perpendicular to the major axis of the ellipse.
No, the foci of an ellipse must always be located inside the ellipse. This is because the sum of the distances from any point on the ellipse to the two foci is constant and equal to the length of the major axis.
The distance between the foci of an ellipse determines the shape of the ellipse. If the distance between the foci is larger, the ellipse will be more elongated and closer to a parabola. If the distance between the foci is smaller, the ellipse will be more circular in shape.