Linear Eccentricity of Hyperbola given Eccentricity 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/Eccentricity of Hyperbola^2))
c = sqrt(b^2/(1-1/e^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.
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.
STEP 1: Convert Input(s) to Base Unit
Semi Conjugate Axis of Hyperbola: 12 Meter --> 12 Meter No Conversion Required
Eccentricity of Hyperbola: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
c = sqrt(b^2/(1-1/e^2)) --> sqrt(12^2/(1-1/3^2))
Evaluating ... ...
c = 12.7279220613579
STEP 3: Convert Result to Output's Unit
12.7279220613579 Meter --> No Conversion Required
FINAL ANSWER
12.7279220613579 12.72792 Meter <-- Linear Eccentricity of Hyperbola
(Calculation completed in 00.006 seconds)

Credits

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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6 Linear Eccentricity of Hyperbola Calculators

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

3 Linear Eccentricity of Hyperbola Calculators

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

Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity of Hyperbola^2))
c = sqrt(b^2/(1-1/e^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 Eccentricity and Semi Conjugate Axis?

Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis calculator uses Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity of Hyperbola^2)) to calculate the Linear Eccentricity of Hyperbola, The Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola. Linear Eccentricity of Hyperbola is denoted by c symbol.

How to calculate Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis using this online calculator? To use this online calculator for Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis, enter Semi Conjugate Axis of Hyperbola (b) & Eccentricity of Hyperbola (e) and hit the calculate button. Here is how the Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis calculation can be explained with given input values -> 12.72792 = sqrt(12^2/(1-1/3^2)).

FAQ

What is Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis?
The Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola and is represented as c = sqrt(b^2/(1-1/e^2)) or Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity 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 & 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.
How to calculate Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis?
The Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola is calculated using Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity of Hyperbola^2)). To calculate Linear Eccentricity of Hyperbola given Eccentricity and Semi Conjugate Axis, you need Semi Conjugate Axis of Hyperbola (b) & Eccentricity of Hyperbola (e). With our tool, you need to enter the respective value for Semi Conjugate Axis of Hyperbola & Eccentricity 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 & Eccentricity of Hyperbola. We can use 7 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(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola
  • 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)))
  • Linear Eccentricity of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/Focal Parameter of Hyperbola
  • Linear Eccentricity of Hyperbola = sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)
  • Linear Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola
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