Sum of the focal distances of a point on an ellipse whose...

Sum of the focal distances of a point on an ellipse whose major and minor axes are of lengths $2 \mathrm{a}$ and $2 \mathrm{~b}$ respectively, is equal to
(a) 2a
(b) $2 \mathrm{~b}$
(c) $2 \mathrm{ae}$
(d) $2 \mathrm{ab}$

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Key Concepts

Ellipse

An ellipse is a curve in a plane defined as the set of all points for which the sum of the distances to two fixed points, called foci, is constant. This fundamental definition is key to understanding many of its geometric properties.

Major Axis

The major axis of an ellipse is the longest line segment that passes through its center and connects two points on the ellipse. It directly relates to the constant sum property, as the sum of the distances from any point on the ellipse to the foci equals the length of the major axis.

Foci

The foci are two specific points on the interior of an ellipse. By the defining property of an ellipse, the total distance from any point on the ellipse to these two foci remains constant, which is a central characteristic in the study of conic sections.

Constant Sum Property

This property states that for any point on the ellipse, the sum of the distances to the two foci is constant and equals the length of the major axis. This concept is crucial in the derivation and understanding of many other properties of ellipses.

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