Ellipse: Eccentricity, Latus Rectum, and Major/Minor Axes An ellipse is a plane curve that is defined by a set of points such that the distance from a fixed...
An ellipse is a plane curve that is defined by a set of points such that the distance from a fixed point (the center) is equal to the distances from the center to two other points. The distance from the center to the closer point is called the radius and is indicated by r. The distance from the center to the farthest point is called the semi-major axis and is indicated by a. The distance from the center to the focus is called the semi-minor axis and is indicated by b.
Eccentricity measures how stretched or compressed an ellipse is compared to a circle. An ellipse with an eccentricity less than 1 is more stretched than a circle, while an ellipse with an eccentricity greater than 1 is more compressed than a circle. The eccentricity is determined by the ratio of the major axis length (a) to the minor axis length (b).
The latus rectum is a straight line segment that connects the center of an ellipse to a focus. The major axis and minor axis intersect the latus rectum at right angles, and the center of the ellipse lies on the perpendicular bisector of the angles formed by the major and minor axes.
The major axis and minor axis are parallel and of equal length. The major axis is the longest axis of the ellipse, and the minor axis is shorter but still longer than the radius. The center of the ellipse is located at the midpoint between the foci.
An ellipse can be classified as ellipse, circle, or hyperbola based on the relative values of the major and minor axis lengths