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Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Formula

GoLinear Eccentricity of Hyperbola Formula

GoLinear Eccentricity of Hyperbola given Eccentricity and Semi Transverse Axis Formula

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Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola. Check FAQs

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

c - Linear Eccentricity of Hyperbola?b - Semi Conjugate Axis of Hyperbola?L - Latus Rectum of Hyperbola?

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Example

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

12.9244 = \sqrt{\frac{12^{2}}{1 - \frac{1}{1 + \frac{{(60)}^{2}}{{(2 \cdot 12)}^{2}}}}}

12.9244m = \sqrt{\frac{{12m}^{2}}{1 - \frac{1}{1 + \frac{{(60m)}^{2}}{{(2 \cdot 12m)}^{2}}}}}

12.9244 = \sqrt{\frac{12^{2}}{1 - \frac{1}{1 + \frac{{(60)}^{2}}{{(2 \cdot 12)}^{2}}}}}

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Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

c = \sqrt{\frac{{12m}^{2}}{1 - \frac{1}{1 + \frac{{(60m)}^{2}}{{(2 \cdot 12m)}^{2}}}}}

Next Step Prepare to Evaluate

∴

c = \sqrt{\frac{12^{2}}{1 - \frac{1}{1 + \frac{{(60)}^{2}}{{(2 \cdot 12)}^{2}}}}}

Next Step Evaluate

∴

c = 12.9243955371228m

LAST Step Rounding Answer

∴

c = 12.9244m

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Formula Elements

Variables

Functions

Linear Eccentricity of Hyperbola

Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola.

Symbol: c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Linear 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

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

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 Linear Eccentricity of Hyperbola

Go Linear Eccentricity of Hyperbola

c = \sqrt{a^{2} + b^{2}}

Go Linear Eccentricity of Hyperbola given Eccentricity and Semi Transverse Axis

c = e \cdot a

Go Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis

c = \sqrt{\frac{b^{2}}{1 - \frac{1}{e^{2}}}}

Go Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis

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

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

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis evaluator uses Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2))) to evaluate the Linear Eccentricity of Hyperbola, The Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the latus rectum and semi-conjugate axis of the Hyperbola. Linear Eccentricity of Hyperbola is denoted by c symbol.

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

FAQs on Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis

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

The formula of Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis is expressed as Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2))). Here is an example- 12.9244 = sqrt(12^2/(1-1/(1+(60)^2/(2*12)^2))).

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

With Semi Conjugate Axis of Hyperbola (b) & Latus Rectum of Hyperbola (L) we can find Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis using the formula - Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Linear Eccentricity of Hyperbola?

Here are the different ways to Calculate Linear Eccentricity of Hyperbola-

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

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

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

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

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis can be measured.

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Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Formula

​GoLinear Eccentricity of Hyperbola Formula

​GoLinear Eccentricity of Hyperbola given Eccentricity and Semi Transverse Axis Formula

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Example

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Solution

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis Formula Elements

Other Formulas to find Linear Eccentricity of Hyperbola

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

FAQs on Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis

Variable Name

GoLinear Eccentricity of Hyperbola Formula

GoLinear Eccentricity of Hyperbola given Eccentricity and Semi Transverse Axis Formula