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An ellipse is a geometric shape that belongs to the family of curves called conic sections. It is characterized by its two focus points (F1 and F2) and every point (P) on its boundary (ellipse curve). The main property of an ellipse is that the sum of distances from any point P on its boundary to the two foci is constant.

Let F1 and F2 be the two foci of an ellipse, and P be any point on the ellipse. Then, the sum of the distances PF1 and PF2 is constant and equal to the length of the major axis of the ellipse (2a). Mathematically, this is written as: PF1 + PF2 = 2a [Here, a represents the distance between the center of the ellipse and one of its vertices.]

Besides the foci, an ellipse has other parameters like the major axis, vertical axis, and the eccentricity. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter, both intersecting at the center of the ellipse. The eccentricity (e) is a dimensionless quantity that characterizes the shape of the ellipse and is connected to the foci through the formula: e = sqrt(1 - (b^2 / a^2)) [Here, b is the distance between the center and one of the endpoints of the minor axis.] Now, you have a clear understanding of the property that defines all ellipses and its key characteristics. The fundamental property that defines an ellipse is that the sum of the distances from any point P on its boundary to the two foci F1 and F2 is constant and equal to the length of the major axis (2a): PF1 + PF2 = 2a.