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Eccentricity of Hyperbola Formula

GoEccentricity of Hyperbola given Focal Parameter Formula

GoEccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis Formula

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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. Check FAQs

e = \sqrt{1 + \frac{b^{2}}{a^{2}}}

e - Eccentricity of Hyperbola?b - Semi Conjugate Axis of Hyperbola?a - Semi Transverse Axis of Hyperbola?

Eccentricity of Hyperbola Example

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Here is how the Eccentricity of Hyperbola equation looks like with Values.

Here is how the Eccentricity of Hyperbola equation looks like with Units.

Here is how the Eccentricity of Hyperbola equation looks like.

2.6 = \sqrt{1 + \frac{12^{2}}{5^{2}}}

2.6m = \sqrt{1 + \frac{{12m}^{2}}{{5m}^{2}}}

2.6 = \sqrt{1 + \frac{12^{2}}{5^{2}}}

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Eccentricity of Hyperbola Solution

Follow our step by step solution on how to calculate Eccentricity of Hyperbola?

FIRST Step Consider the formula

e = \sqrt{1 + \frac{b^{2}}{a^{2}}}

Next Step Substitute values of Variables

∴

e = \sqrt{1 + \frac{{12m}^{2}}{{5m}^{2}}}

Next Step Prepare to Evaluate

∴

e = \sqrt{1 + \frac{12^{2}}{5^{2}}}

LAST Step Evaluate

∴

e = 2.6m

Eccentricity of Hyperbola Formula Elements

Variables

Functions

Eccentricity of Hyperbola

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.

Symbol: e

Measurement: LengthUnit: m

Note: Value should be greater than 1.

Formulas to find Eccentricity of Hyperbola

Semi Conjugate Axis of Hyperbola

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.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Conjugate Axis of Hyperbola

Semi Transverse Axis of Hyperbola

Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.

Symbol: a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Transverse Axis of Hyperbola

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.

Syntax: sqrt(Number)

Other Formulas to find Eccentricity of Hyperbola

Go Eccentricity of Hyperbola given Focal Parameter

e = \frac{b^{2}}{a \cdot p}

Go Eccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis

e = \frac{c}{a}

Go Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis

e = \sqrt{1 + \frac{{(L)}^{2}}{{(2 \cdot b)}^{2}}}

How to Evaluate Eccentricity of Hyperbola?

Eccentricity of Hyperbola evaluator uses Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2)) to evaluate 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 evaluate Eccentricity of Hyperbola using this online evaluator? To use this online evaluator for Eccentricity of Hyperbola, enter Semi Conjugate Axis of Hyperbola (b) & Semi Transverse Axis of Hyperbola (a) and hit the calculate button.

FAQs on Eccentricity of Hyperbola

What is the formula to find Eccentricity of Hyperbola?

The formula of Eccentricity of Hyperbola is expressed as Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2)). Here is an example- 2.6 = sqrt(1+(12^2)/(5^2)).

How to calculate Eccentricity of Hyperbola?

With Semi Conjugate Axis of Hyperbola (b) & Semi Transverse Axis of Hyperbola (a) we can find Eccentricity of Hyperbola using the formula - Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Eccentricity of Hyperbola?

Here are the different ways to Calculate Eccentricity of Hyperbola-

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)

Can the Eccentricity of Hyperbola be negative?

No, the Eccentricity of Hyperbola, measured in Length cannot be negative.

Which unit is used to measure Eccentricity of Hyperbola?

Eccentricity of Hyperbola is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Eccentricity of Hyperbola can be measured.

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Eccentricity of Hyperbola Formula

​GoEccentricity of Hyperbola given Focal Parameter Formula

​GoEccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis Formula

Eccentricity of Hyperbola Example

Eccentricity of Hyperbola Solution

Eccentricity of Hyperbola Formula Elements

Other Formulas to find Eccentricity of Hyperbola

How to Evaluate Eccentricity of Hyperbola?

FAQs on Eccentricity of Hyperbola

Variable Name

GoEccentricity of Hyperbola given Focal Parameter Formula

GoEccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis Formula