Definition of Eccentricity:

Eccentricity is a mathematical term that refers to the measure of how elongated or stretched out an ellipse or conic section is.

Types of Eccentricity:

1. Linear Eccentricity:

The linear eccentricity of an ellipse or conic section is the distance between the center and one of the foci of the shape.

2. Eccentricity of an Ellipse:

The eccentricity of an ellipse is a ratio determined by the distance between the center and one of the foci divided by the semi-major axis of the ellipse. It lies between 0 and 1, where 0 represents a circle and 1 represents a line.

3. Eccentricity of a Hyperbola:

The eccentricity of a hyperbola is a ratio determined by the distance between the center and one of the foci divided by the distance between the center and a vertex. It is always greater than 1.

Significance of Eccentricity:

Eccentricity plays a crucial role in the study of conic sections. It helps in determining the shape of ellipses, parabolas, and hyperbolas, and understanding their unique properties and characteristics. In astronomy, eccentricity is used to describe the shape of orbits of celestial bodies around a central object, such as planets orbiting the Sun.