Semi Transverse Axis of Hyperbola given Eccentricity 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%
✖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.ⓘ Eccentricity of Hyperbola [e]			+10% -10%

✖Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.ⓘ Semi Transverse Axis of Hyperbola given Eccentricity [a]

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Semi Transverse Axis of Hyperbola given Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Semi Transverse Axis of Hyperbola - (Measured in Meter) - Semi Transverse Axis of Hyperbola is half of the distance between the vertices 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

a = b/sqrt(e^2-1) --> 12/sqrt(3^2-1)

Evaluating ... ...

a = 4.24264068711928

STEP 3: Convert Result to Output's Unit

4.24264068711928 Meter --> No Conversion Required

FINAL ANSWER

4.24264068711928 ≈ 4.242641 Meter <-- Semi Transverse 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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< Transverse Axis of Hyperbola Calculators

Semi Transverse Axis of Hyperbola given Eccentricity

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

Semi Transverse Axis of Hyperbola given Latus Rectum

LaTeX Go Semi Transverse Axis of Hyperbola = (2*Semi Conjugate Axis of Hyperbola^2)/Latus Rectum of Hyperbola

Semi Transverse Axis of Hyperbola

LaTeX Go Semi Transverse Axis of Hyperbola = Transverse Axis of Hyperbola/2

Transverse Axis of Hyperbola

LaTeX Go Transverse Axis of Hyperbola = 2*Semi Transverse Axis of Hyperbola

Semi Transverse Axis of Hyperbola given Eccentricity Formula

LaTeX Go

Semi Transverse Axis of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1)
a = b/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 Transverse Axis of the Hyperbola and how is it calculated?

The transverse axis is actually the major axis of the Hyperbola. It is the line segment that passes through the center of the Hyperbola and has vertices as its endpoints. It is double the semi-transverse axis of the Hyperbola, and it is denoted by 2a. And a denotes the semi-transverse axis of the Hyperbola, which has more role in the formulas.

How to Calculate Semi Transverse Axis of Hyperbola given Eccentricity?

Semi Transverse Axis of Hyperbola given Eccentricity calculator uses Semi Transverse Axis of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1) to calculate the Semi Transverse Axis of Hyperbola, The Semi Transverse Axis of Hyperbola given Eccentricity formula is defined as half of the line segment joining two vertices of the Hyperbola and is calculated using the eccentricity and the semi-conjugate axis of the Hyperbola. Semi Transverse Axis of Hyperbola is denoted by a symbol.

How to calculate Semi Transverse Axis of Hyperbola given Eccentricity using this online calculator? To use this online calculator for Semi Transverse Axis of Hyperbola given Eccentricity, enter Semi Conjugate Axis of Hyperbola (b) & Eccentricity of Hyperbola (e) and hit the calculate button. Here is how the Semi Transverse Axis of Hyperbola given Eccentricity calculation can be explained with given input values -> 4.242641 = 12/sqrt(3^2-1).

FAQ

What is Semi Transverse Axis of Hyperbola given Eccentricity?

The Semi Transverse Axis of Hyperbola given Eccentricity formula is defined as half of the line segment joining two vertices of the Hyperbola and is calculated using the eccentricity and the semi-conjugate axis of the Hyperbola and is represented as a = b/sqrt(e^2-1) or Semi Transverse Axis of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1). 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 Semi Transverse Axis of Hyperbola given Eccentricity?

The Semi Transverse Axis of Hyperbola given Eccentricity formula is defined as half of the line segment joining two vertices of the Hyperbola and is calculated using the eccentricity and the semi-conjugate axis of the Hyperbola is calculated using Semi Transverse Axis of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1). To calculate Semi Transverse Axis of Hyperbola given Eccentricity, 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 Semi Transverse Axis of Hyperbola?

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

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

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