Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis 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%
✖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.ⓘ Latus Rectum of Hyperbola [L]			+10% -10%

✖Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola.ⓘ Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis [c]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)))
c = sqrt(b^2/(1-1/(1+(L)^2/(2*b)^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

Linear Eccentricity of Hyperbola - (Measured in Meter) - Linear Eccentricity of Hyperbola is half of the distance between foci 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.
Latus Rectum of Hyperbola - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Semi Conjugate Axis of Hyperbola: 12 Meter --> 12 Meter No Conversion Required
Latus Rectum of Hyperbola: 60 Meter --> 60 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

c = sqrt(b^2/(1-1/(1+(L)^2/(2*b)^2))) --> sqrt(12^2/(1-1/(1+(60)^2/(2*12)^2)))

Evaluating ... ...

c = 12.9243955371228

STEP 3: Convert Result to Output's Unit

12.9243955371228 Meter --> No Conversion Required

FINAL ANSWER

12.9243955371228 ≈ 12.9244 Meter <-- Linear Eccentricity of Hyperbola

(Calculation completed in 00.020 seconds)

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< Linear Eccentricity of Hyperbola Calculators

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis

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

Linear Eccentricity of Hyperbola

LaTeX Go Linear Eccentricity of Hyperbola = sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)

Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis

LaTeX Go Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity of Hyperbola^2))

Linear Eccentricity of Hyperbola given Eccentricity and Semi Transverse Axis

LaTeX Go Linear Eccentricity of Hyperbola = Eccentricity of Hyperbola*Semi Transverse Axis of Hyperbola

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

LaTeX Go

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)))
c = sqrt(b^2/(1-1/(1+(L)^2/(2*b)^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 the Linear Eccentricity of Hyperbola and how it is calculated?

The linear eccentricity (c) is the distance between the center and a focus of the Hyperbola. Otherwise, linear eccentricity of Hyperbola is half of the distance between foci of the Hyperbola. It is calculated by the formula c = √((a²)+(b²)) where c is the linear eccentricity of the Hyperbola, a is the semi transverse axis of the Hyperbola and b is the semi conjugate axis of the Hyperbola.

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

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis calculator 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 calculate 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 calculate Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis using this online calculator? To use this online calculator 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. Here is how the Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis calculation can be explained with given input values -> 12.9244 = sqrt(12^2/(1-1/(1+(60)^2/(2*12)^2))).

FAQ

What is Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis?

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 and is represented as c = sqrt(b^2/(1-1/(1+(L)^2/(2*b)^2))) or 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))). 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 & 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.

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

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 is calculated using 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 calculate Linear Eccentricity of Hyperbola given Latus Rectum and Semi Conjugate Axis, you need Semi Conjugate Axis of Hyperbola (b) & Latus Rectum of Hyperbola (L). With our tool, you need to enter the respective value for Semi Conjugate Axis of Hyperbola & Latus Rectum 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 Linear Eccentricity of Hyperbola?

In this formula, Linear Eccentricity of Hyperbola uses Semi Conjugate Axis of Hyperbola & Latus Rectum of Hyperbola. We can use 3 other way(s) to calculate the same, which is/are as follows -

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))

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