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## Credits

Birsa Institute of Technology (BIT), Sindri
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## Eccentricity of hyperbola Solution

STEP 0: Pre-Calculation Summary
Formula Used
eccentricity = sqrt(1+((Semi-minor axis)^2/(Semi-major axis)^2))
e = sqrt(1+((b)^2/(a)^2))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Semi-minor axis - Semi-minor axis of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section. (Measured in Centimeter)
Semi-major axis - Semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Semi-minor axis: 10 Centimeter --> 0.1 Meter (Check conversion here)
Semi-major axis: 10 Centimeter --> 0.1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
e = sqrt(1+((b)^2/(a)^2)) --> sqrt(1+((0.1)^2/(0.1)^2))
Evaluating ... ...
e = 1.4142135623731
STEP 3: Convert Result to Output's Unit
1.4142135623731 Meter -->141.42135623731 Centimeter (Check conversion here)
141.42135623731 Centimeter <-- Eccentricity
(Calculation completed in 00.031 seconds)

## < 11 Other formulas that you can solve using the same Inputs

Length of radius vector from center in given direction whose angle is theta in ellipse
length = sqrt((Semi-major axis^2)*(Semi-minor axis^2)/(Semi-minor axis^2+(Semi-major axis^2-Semi-minor axis^2)*(sin(Angle))^2)) Go
Focal parameter of the hyperbola
focal_parameter_of_an_ellipse = (Semi-minor axis)^2/sqrt((Semi-major axis)^2+(Semi-minor axis)^2) Go
Value of lambda of semi-ellipse
lambda = (Semi-major axis-Height)/(Semi-major axis+Height) Go
Linear eccentricity of the hyperbola
linear_eccentricity = sqrt((Semi-major axis)^2+(Semi-minor axis)^2) Go
Semi-major axis of an ellipse
semimajor_axis = sqrt((Semi-minor axis)^2+(Linear Eccentricity)^2) Go
Semi-minor axis of an ellipse
semiminor_axis = sqrt((Semi-major axis)^2-(Linear Eccentricity)^2) Go
The length of the semi - minor axis if eccentricity is given
semiminor_axis = sqrt(Eccentricity^2-1)*Semi-major axis Go
Area of semi-ellipse
area = (pi/2)*Semi-major axis*Height Go
Semi-latus rectum of an ellipse when eccentricity is given
semilatus_rectum = Semi-major axis*(1-(Eccentricity)^2) Go
Semi-latus rectum of hyperbola
semilatus_rectum = (Semi-minor axis)^2/Semi-major axis Go
Linear eccentricity of an ellipse when eccentricity and semimajor axis are given
linear_eccentricity = (Eccentricity*Semi-major axis) Go

## < 11 Other formulas that calculate the same Output

Kepler's First Law
eccentricity = sqrt((Semi-major axis^2-Semi-minor axis^2))/Semi-major axis Go
Eccentricity of Bearing in Terms of Minimum Film Thickness
Eccentricity of an ellipse (a>b)
eccentricity = sqrt(1-((Minor axis)^2/(Major axis)^2)) Go
Eccentricity of an ellipse (b>a)
eccentricity = sqrt(1-((Minor axis)^2/(Major axis)^2)) Go
Eccentricity if moment due to eccentric load is given
eccentricity between central and neutral axis
Eccentricity of Slender Columns
eccentricity = Magnified moment/Axial Load Capacity Go
Eccentricity of a Bearing in Terms of Radial Clearance and Eccentricity
eccentricity = Radial Clearance*Eccentricity Ratio Go
Eccentricity of an ellipse when linear eccentricity is given
eccentricity = (Linear Eccentricity)/Major axis Go
Eccentricity of hyperbola when linear eccentricity is given
eccentricity = Linear Eccentricity/Major axis Go
Eccentricity for solid circular sector to maintain stress as wholly compressive
eccentricity = Diameter/8 Go

### Eccentricity of hyperbola Formula

eccentricity = sqrt(1+((Semi-minor axis)^2/(Semi-major axis)^2))
e = sqrt(1+((b)^2/(a)^2))

## What is eccentricity of the hyperbola and how it is calculated?

The eccentricity of a hyperbola is the ratio of the distance from any point on the graph to the focus and the directrix. It is calculated by the formula e = √(1 + b2 / a2) where e is the eccentricity of the hyperbola , b is the semi-minor axis of the hyperbola and a is the semi-major of the hyperbola.

## How to Calculate Eccentricity of hyperbola?

Eccentricity of hyperbola calculator uses eccentricity = sqrt(1+((Semi-minor axis)^2/(Semi-major axis)^2)) to calculate the Eccentricity, Eccentricity of hyperbola is the ratio of the distance from any point on the graph to the focus and the directrix. Eccentricity and is denoted by e symbol.

How to calculate Eccentricity of hyperbola using this online calculator? To use this online calculator for Eccentricity of hyperbola, enter Semi-minor axis (b) and Semi-major axis (a) and hit the calculate button. Here is how the Eccentricity of hyperbola calculation can be explained with given input values -> 141.4214 = sqrt(1+((0.1)^2/(0.1)^2)).

### FAQ

What is Eccentricity of hyperbola?
Eccentricity of hyperbola is the ratio of the distance from any point on the graph to the focus and the directrix and is represented as e = sqrt(1+((b)^2/(a)^2)) or eccentricity = sqrt(1+((Semi-minor axis)^2/(Semi-major axis)^2)). Semi-minor axis of an ellipse or hyperbola is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section and Semi-major axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter.
How to calculate Eccentricity of hyperbola?
Eccentricity of hyperbola is the ratio of the distance from any point on the graph to the focus and the directrix is calculated using eccentricity = sqrt(1+((Semi-minor axis)^2/(Semi-major axis)^2)). To calculate Eccentricity of hyperbola, you need Semi-minor axis (b) and Semi-major axis (a). With our tool, you need to enter the respective value for Semi-minor axis and Semi-major axis and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Eccentricity?
In this formula, Eccentricity uses Semi-minor axis and Semi-major axis. We can use 11 other way(s) to calculate the same, which is/are as follows -
• eccentricity = sqrt(1-((Minor axis)^2/(Major axis)^2))
• eccentricity = sqrt(1-((Minor axis)^2/(Major axis)^2))
• eccentricity = (Linear Eccentricity)/Major axis
• eccentricity = Linear Eccentricity/Major axis
• eccentricity = Magnified moment/Axial Load Capacity 