Eccentricity of Ellipse
An ellipse is a closed curve that is symmetric with respect to two perpendicular axes. It can also be defined as the set of all points in a plane, such that the sum of the distances from any point on the curve to two fixed points (called foci) is constant.
Elements of Ellipse
- Centre: The midpoint of both major and minor axes, specifying the ellipse’s centre.
- Major Axis: The longer diameter passing through the centre, determining the ellipse’s length.
- Minor Axis: The shorter diameter perpendicular to the major axis, establishing the ellipse’s width.
Eccentricity of Ellipse
Therefore,
Eccentricity of ellipse is greater than zero but less than one i.e. (0 < e < 1).
General equation of an Ellipse is
x2/a2 + y2/b2= 1
Eccentricity of Ellipse Formula
Ellipse Eccentricity Formula is
e = √(a2– b2)/a2
where,
- a is length of Semi-Major Axis
- b is Length of Semi-Minor Axis
Eccentricity Formula of Circle, Parabola, Ellipse, Hyperbola
Eccentricity is a non-negative real number that describes the shape of a conic section. It measures how much a conic section deviates from being circular. Generally, eccentricity measures the degree to which a conic section differs from a uniform circular shape.
Let’s discuss Eccentricity formula for circle, parabola, ellipse, and hyperbola, along with examples.
Eccentricity in Conic Sections
Table of Content
- Eccentricity in Geometry
- Eccentricity Formula
- Eccentricity of Circle
- Eccentricity of Parabola
- Eccentricity of Ellipse
- Eccentricity of Hyperbola
- Eccentricity of Conic Sections
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