Eccentricity of Hyperbola Calculator

✖Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola.ⓘ Semi Conjugate Axis of Hyperbola [b]			+10% -10%
✖Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.ⓘ Semi Transverse Axis of Hyperbola [a]			+10% -10%

✖Eccentricity of Hyperbola is the ratio of distances of any point on the Hyperbola from focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola.ⓘ Eccentricity of Hyperbola [e]

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Formula

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Eccentricity of Hyperbola

Formula

`"e" = sqrt(1+("b"^2)/("a"^2))`

Example

`"2.6m"=sqrt(1+(("12m")^2)/(("5m")^2))`

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Eccentricity of Hyperbola Solution

STEP 0: Pre-Calculation Summary

Formula Used

Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2))
e = sqrt(1+(b^2)/(a^2))
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Eccentricity of Hyperbola - (Measured in Meter) - Eccentricity of Hyperbola is the ratio of distances of any point on the Hyperbola from focus and the directrix, or it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola.
Semi Conjugate Axis of Hyperbola - (Measured in Meter) - Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola.
Semi Transverse Axis of Hyperbola - (Measured in Meter) - Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.

STEP 1: Convert Input(s) to Base Unit

Semi Conjugate Axis of Hyperbola: 12 Meter --> 12 Meter No Conversion Required
Semi Transverse Axis of Hyperbola: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e = sqrt(1+(b^2)/(a^2)) --> sqrt(1+(12^2)/(5^2))

Evaluating ... ...

e = 2.6

STEP 3: Convert Result to Output's Unit

2.6 Meter --> No Conversion Required

FINAL ANSWER

2.6 Meter <-- Eccentricity of Hyperbola

(Calculation completed in 00.004 seconds)

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Birsa Institute of Technology (BIT), Sindri

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< 7 Eccentricity of Hyperbola Calculators

Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis

Go Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2)

Eccentricity of Hyperbola given Focal Parameter and Semi Conjugate Axis

Go Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Semi Conjugate Axis of Hyperbola^2-Focal Parameter of Hyperbola^2)

Eccentricity of Hyperbola given Focal Parameter

Go Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola^2/(Semi Transverse Axis of Hyperbola*Focal Parameter of Hyperbola)

Eccentricity of Hyperbola

Go Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2))

Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis

Go Eccentricity of Hyperbola = sqrt(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2)

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis

Go Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))

Eccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis

Go Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola

< 4 Eccentricity of Hyperbola Calculators

Eccentricity of Hyperbola given Focal Parameter

Go Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola^2/(Semi Transverse Axis of Hyperbola*Focal Parameter of Hyperbola)

Eccentricity of Hyperbola

Go Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2))

Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis

Go Eccentricity of Hyperbola = sqrt(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2)

Eccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis

Go Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola

Eccentricity of Hyperbola Formula

Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2))
e = sqrt(1+(b^2)/(a^2))

What is Hyperbola?

A Hyperbola is a type of conic section, which is a geometric figure that results from intersecting a cone with a plane. A Hyperbola is defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is constant. In other words, a Hyperbola is the locus of points where the difference between the distances to two fixed points is a constant value. The standard form of the equation for a Hyperbola is: (x - h)²/a² - (y - k)²/b² = 1

What is Eccentricity of the Hyperbola and how is it calculated?

The eccentricity of a Hyperbola is the ratio of the distances from any point on the Hyperbola to the focus and the corresponding directrix. It is calculated by the formula e = c/a where e is the eccentricity of the Hyperbola, c is the linear eccentricity of the Hyperbola and a is the semi-transverse of the Hyperbola.

How to Calculate Eccentricity of Hyperbola?

Eccentricity of Hyperbola calculator uses Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2)) to calculate the Eccentricity of Hyperbola, Eccentricity of Hyperbola formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, or simply it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola. Eccentricity of Hyperbola 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 Conjugate Axis of Hyperbola (b) & Semi Transverse Axis of Hyperbola (a) and hit the calculate button. Here is how the Eccentricity of Hyperbola calculation can be explained with given input values -> 2.6 = sqrt(1+(12^2)/(5^2)).

FAQ

What is Eccentricity of Hyperbola?

Eccentricity of Hyperbola formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, or simply it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola and is represented as e = sqrt(1+(b^2)/(a^2)) or Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2)). Semi Conjugate Axis of Hyperbola is half of the tangent from any of the vertices of the Hyperbola and chord to the circle passing through the foci and centered at the center of the Hyperbola & Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.

How to calculate Eccentricity of Hyperbola?

Eccentricity of Hyperbola formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, or simply it is the ratio of linear eccentricity and semi transverse axis of the Hyperbola is calculated using Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2)). To calculate Eccentricity of Hyperbola, you need Semi Conjugate Axis of Hyperbola (b) & Semi Transverse Axis of Hyperbola (a). With our tool, you need to enter the respective value for Semi Conjugate Axis of Hyperbola & Semi Transverse Axis of Hyperbola 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 of Hyperbola?

In this formula, Eccentricity of Hyperbola uses Semi Conjugate Axis of Hyperbola & Semi Transverse Axis of Hyperbola. We can use 9 other way(s) to calculate the same, which is/are as follows -

Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola
Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2)
Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))
Eccentricity of Hyperbola = sqrt(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2)
Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola^2/(Semi Transverse Axis of Hyperbola*Focal Parameter of Hyperbola)
Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Semi Conjugate Axis of Hyperbola^2-Focal Parameter of Hyperbola^2)
Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola^2/(Semi Transverse Axis of Hyperbola*Focal Parameter of Hyperbola)
Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola
Eccentricity of Hyperbola = sqrt(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2)

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