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Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Formula

GoEccentricity of Hyperbola 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{L}{2 \cdot a}}

e - Eccentricity of Hyperbola?L - Latus Rectum of Hyperbola?a - Semi Transverse Axis of Hyperbola?

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Example

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Here is how the Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis equation looks like with Values.

Here is how the Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis equation looks like with Units.

Here is how the Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis equation looks like.

2.6458 = \sqrt{1 + \frac{60}{2 \cdot 5}}

2.6458m = \sqrt{1 + \frac{60m}{2 \cdot 5m}}

2.6458 = \sqrt{1 + \frac{60}{2 \cdot 5}}

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Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Solution

Follow our step by step solution on how to calculate Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?

FIRST Step Consider the formula

e = \sqrt{1 + \frac{L}{2 \cdot a}}

Next Step Substitute values of Variables

∴

e = \sqrt{1 + \frac{60m}{2 \cdot 5m}}

Next Step Prepare to Evaluate

∴

e = \sqrt{1 + \frac{60}{2 \cdot 5}}

Next Step Evaluate

∴

e = 2.64575131106459m

LAST Step Rounding Answer

∴

e = 2.6458m

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis 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

Latus Rectum of Hyperbola

Latus Rectum of Hyperbola is the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Latus Rectum 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)

Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Formula and 1100+ more formulas!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Formula and 1500+ more formulas!

Other Formulas to find Eccentricity of Hyperbola

Go Eccentricity of Hyperbola

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

Go Eccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis

e = \frac{c}{a}

Go Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis

e = \frac{c}{\sqrt{c^{2} - b^{2}}}

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 given Latus Rectum and Semi Transverse Axis?

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis evaluator uses Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola)) to evaluate the Eccentricity of Hyperbola, The Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, and is calculated using the latus rectum and semi-transverse axis of the Hyperbola. Eccentricity of Hyperbola is denoted by e symbol.

How to evaluate Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis using this online evaluator? To use this online evaluator for Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis, enter Latus Rectum of Hyperbola (L) & Semi Transverse Axis of Hyperbola (a) and hit the calculate button.

FAQs on Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis

What is the formula to find Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?

The formula of Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis is expressed as Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola)). Here is an example- 2.645751 = sqrt(1+60/(2*5)).

How to calculate Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?

With Latus Rectum of Hyperbola (L) & Semi Transverse Axis of Hyperbola (a) we can find Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis using the formula - Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola)). 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=sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2))
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)

Can the Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis be negative?

No, the Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis, measured in Length cannot be negative.

Which unit is used to measure Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis 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 given Latus Rectum and Semi Transverse Axis can be measured.

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Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Formula

​GoEccentricity of Hyperbola Formula

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

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Example

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Solution

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Formula Elements

Credits

Other Formulas to find Eccentricity of Hyperbola

How to Evaluate Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?

FAQs on Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis

Variable Name

GoEccentricity of Hyperbola Formula

GoEccentricity of Hyperbola given Linear Eccentricity and Semi Transverse Axis Formula