Eccentricity Formula
Eccentricity formula of different shapes is as follows:
Eccentricity (e) = c/a
where,
- c = Distance between Any point on Conic Section and Focus
- a = Distance between Any point on Conic Section and Directrix
The Eccentricity formula for different shapes is tabulated below:
Eccentricity Formulas |
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---|---|---|
Shape | Equation | Eccentricity |
Circle | √[(x –h)2+( y–k)2]= r | e = 0 |
Parabola | y = a(x-h)2 + k | e = 1 |
Ellipse | x2 /a2 +y2/b2= 1 |
If a > b, e = √(a2-b2)/a2 If b > a, e = √(b2 – a2)/b2 |
Hyperbola | x2 /a2 – y2/b2= 1 | √(a2+b2)/a2 |
Now let us learn the Eccentricity of different conic sections, namely Circle, Parabola, Ellipse, and Hyperbola.
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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