Semi Conjugate Axis of Hyperbola given Eccentricity Solution

STEP 0: Pre-Calculation Summary
Formula Used
Semi Conjugate Axis of Hyperbola = Semi Transverse Axis of Hyperbola*sqrt(Eccentricity of Hyperbola^2-1)
b = a*sqrt(e^2-1)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
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.
Semi Transverse Axis of Hyperbola - (Measured in Meter) - Semi Transverse Axis of Hyperbola is half of the distance between the vertices 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 Transverse Axis of Hyperbola: 5 Meter --> 5 Meter No Conversion Required
Eccentricity of Hyperbola: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
b = a*sqrt(e^2-1) --> 5*sqrt(3^2-1)
Evaluating ... ...
b = 14.142135623731
STEP 3: Convert Result to Output's Unit
14.142135623731 Meter --> No Conversion Required
FINAL ANSWER
14.142135623731 14.14214 Meter <-- Semi Conjugate Axis of Hyperbola
(Calculation completed in 00.004 seconds)

Credits

Created by Shashwati Tidke
Vishwakarma Institute of Technology (VIT), Pune
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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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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

6 Axis of Hyperbola Calculators

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

Semi Conjugate Axis of Hyperbola given Eccentricity Formula

Semi Conjugate Axis of Hyperbola = Semi Transverse Axis of Hyperbola*sqrt(Eccentricity of Hyperbola^2-1)
b = a*sqrt(e^2-1)

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 Semi Conjugate Axis of Hyperbola given Eccentricity?

Semi Conjugate Axis of Hyperbola given Eccentricity calculator uses Semi Conjugate Axis of Hyperbola = Semi Transverse Axis of Hyperbola*sqrt(Eccentricity of Hyperbola^2-1) to calculate the Semi Conjugate Axis of Hyperbola, Semi Conjugate Axis of Hyperbola given Eccentricity formula is defined as 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, and is calculated using the eccentricity and the semi transverse axis of the Hyperbola. Semi Conjugate Axis of Hyperbola is denoted by b symbol.

How to calculate Semi Conjugate Axis of Hyperbola given Eccentricity using this online calculator? To use this online calculator for Semi Conjugate Axis of Hyperbola given Eccentricity, enter Semi Transverse Axis of Hyperbola (a) & Eccentricity of Hyperbola (e) and hit the calculate button. Here is how the Semi Conjugate Axis of Hyperbola given Eccentricity calculation can be explained with given input values -> 14.14214 = 5*sqrt(3^2-1).

FAQ

What is Semi Conjugate Axis of Hyperbola given Eccentricity?
Semi Conjugate Axis of Hyperbola given Eccentricity formula is defined as 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, and is calculated using the eccentricity and the semi transverse axis of the Hyperbola and is represented as b = a*sqrt(e^2-1) or Semi Conjugate Axis of Hyperbola = Semi Transverse Axis of Hyperbola*sqrt(Eccentricity of Hyperbola^2-1). Semi Transverse Axis of Hyperbola is half of the distance between the vertices 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 Semi Conjugate Axis of Hyperbola given Eccentricity?
Semi Conjugate Axis of Hyperbola given Eccentricity formula is defined as 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, and is calculated using the eccentricity and the semi transverse axis of the Hyperbola is calculated using Semi Conjugate Axis of Hyperbola = Semi Transverse Axis of Hyperbola*sqrt(Eccentricity of Hyperbola^2-1). To calculate Semi Conjugate Axis of Hyperbola given Eccentricity, you need Semi Transverse Axis of Hyperbola (a) & Eccentricity of Hyperbola (e). With our tool, you need to enter the respective value for Semi Transverse 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 Semi Conjugate Axis of Hyperbola?
In this formula, Semi Conjugate Axis of Hyperbola uses Semi Transverse Axis of Hyperbola & Eccentricity of Hyperbola. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • Semi Conjugate Axis of Hyperbola = sqrt((Latus Rectum of Hyperbola)^2/(Eccentricity of Hyperbola^2-1))/2
  • Semi Conjugate Axis of Hyperbola = Linear Eccentricity of Hyperbola*sqrt(1-1/Eccentricity of Hyperbola^2)
  • Semi Conjugate Axis of Hyperbola = Conjugate Axis of Hyperbola/2
  • Semi Conjugate Axis of Hyperbola = sqrt((Latus Rectum of Hyperbola*Semi Transverse Axis of Hyperbola)/2)
  • Semi Conjugate Axis of Hyperbola = sqrt(Linear Eccentricity of Hyperbola^2-Semi Transverse Axis of Hyperbola^2)
  • Semi Conjugate Axis of Hyperbola = (Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1))*Focal Parameter of Hyperbola
  • Semi Conjugate Axis of Hyperbola = sqrt(Focal Parameter of Hyperbola*Linear Eccentricity of Hyperbola)
  • 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 = sqrt((Latus Rectum of Hyperbola*Semi Transverse Axis of Hyperbola)/2)
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