Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Conjugate Axis of Hyperbola = 2*Linear Eccentricity of Hyperbola*sqrt(1-1/Eccentricity of Hyperbola^2)
2b = 2*c*sqrt(1-1/e^2)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Conjugate Axis of Hyperbola - (Measured in Meter) - Conjugate Axis of Hyperbola is the line through the center and perpendicular to transverse axis with length of the chord of the circle passing through the foci and touches the Hyperbola at vertex.
Linear Eccentricity of Hyperbola - (Measured in Meter) - Linear Eccentricity of Hyperbola is half of the distance between foci 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
Linear Eccentricity of Hyperbola: 13 Meter --> 13 Meter No Conversion Required
Eccentricity of Hyperbola: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
2b = 2*c*sqrt(1-1/e^2) --> 2*13*sqrt(1-1/3^2)
Evaluating ... ...
2b = 24.5130350811336
STEP 3: Convert Result to Output's Unit
24.5130350811336 Meter --> No Conversion Required
FINAL ANSWER
24.5130350811336 24.51304 Meter <-- Conjugate Axis of Hyperbola
(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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12 Conjugate Axis of Hyperbola Calculators

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

Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity Formula

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

The conjugate axis of Hyperbola is the line perpendicular to the transverse axis and has the co-vertices as its endpoints. It is calculated by the equation c = 2b where c is the length of the conjugate axis of the Hyperbola and b is the semi conjugate axis of the Hyperbola.

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

Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity calculator uses Conjugate Axis of Hyperbola = 2*Linear Eccentricity of Hyperbola*sqrt(1-1/Eccentricity of Hyperbola^2) to calculate the Conjugate Axis of Hyperbola, The Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity formula is defined as the line through the center and perpendicular to transverse axis with length of the chord of the circle passing through the foci and touches the Hyperbola at vertex, and is calculated using the linear eccentricity and eccentricity of the Hyperbola. Conjugate Axis of Hyperbola is denoted by 2b symbol.

How to calculate Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity using this online calculator? To use this online calculator for Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity, enter Linear Eccentricity of Hyperbola (c) & Eccentricity of Hyperbola (e) and hit the calculate button. Here is how the Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity calculation can be explained with given input values -> 24.51304 = 2*13*sqrt(1-1/3^2).

FAQ

What is Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity?
The Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity formula is defined as the line through the center and perpendicular to transverse axis with length of the chord of the circle passing through the foci and touches the Hyperbola at vertex, and is calculated using the linear eccentricity and eccentricity of the Hyperbola and is represented as 2b = 2*c*sqrt(1-1/e^2) or Conjugate Axis of Hyperbola = 2*Linear Eccentricity of Hyperbola*sqrt(1-1/Eccentricity of Hyperbola^2). Linear Eccentricity of Hyperbola is half of the distance between foci 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 Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity?
The Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity formula is defined as the line through the center and perpendicular to transverse axis with length of the chord of the circle passing through the foci and touches the Hyperbola at vertex, and is calculated using the linear eccentricity and eccentricity of the Hyperbola is calculated using Conjugate Axis of Hyperbola = 2*Linear Eccentricity of Hyperbola*sqrt(1-1/Eccentricity of Hyperbola^2). To calculate Conjugate Axis of Hyperbola given Eccentricity and Linear Eccentricity, you need Linear Eccentricity of Hyperbola (c) & Eccentricity of Hyperbola (e). With our tool, you need to enter the respective value for Linear Eccentricity 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 Conjugate Axis of Hyperbola?
In this formula, Conjugate Axis of Hyperbola uses Linear Eccentricity of Hyperbola & Eccentricity of Hyperbola. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Conjugate Axis of Hyperbola = 2*Semi Conjugate Axis of Hyperbola
  • Conjugate Axis of Hyperbola = sqrt((Latus Rectum of Hyperbola)^2/(Eccentricity of Hyperbola^2-1))
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