Eccentricity of Hyperbola
A hyperbola is a conic section that is formed when a plane intersects a double right circular cone at an angle. The intersection produces two separate unbounded curves that are mirror images of each other. A hyperbola is an open curve with two branches. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.
Elements of Hyperbola
- Centre: Midpoint between the two foci, determining the centre of the hyperbola.
- Transverse Axis: Line passing through the foci, establishing the major axis.
- Conjugate Axis: Perpendicular line to the transverse axis, defining the minor axis.
Therefore, Eccentricity of hyperbola is greater than 1, i.e.
e > 1
General equation of a Hyperbola is
x2/a2 – y2/b2= 1
Eccentricity of Hyperbola Formula
Eccentricity Formula for Hyperbola is
e = √(a2+b2)/a2
For any Hyperbola, values of a and b are the lengths of the semi-major and semi-minor axis respectively.
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.
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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