Latus Rectum of Hyperbola given Eccentricity 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%
✖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%

✖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 given Eccentricity and Semi Conjugate Axis [L]

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Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))
L = sqrt((2*b)^2*(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

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.
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

L = sqrt((2*b)^2*(e^2-1)) --> sqrt((2*12)^2*(3^2-1))

Evaluating ... ...

L = 67.8822509939086

STEP 3: Convert Result to Output's Unit

67.8822509939086 Meter --> No Conversion Required

FINAL ANSWER

67.8822509939086 ≈ 67.88225 Meter <-- Latus Rectum of Hyperbola

(Calculation completed in 00.020 seconds)

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< Latus Rectum of Hyperbola Calculators

Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis

LaTeX Go Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))

Latus Rectum of Hyperbola

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

Semi Latus Rectum of Hyperbola

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

Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis

LaTeX Go Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*(Eccentricity of Hyperbola^2-1)

Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis Formula

LaTeX Go

Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))
L = sqrt((2*b)^2*(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 Latus Rectum of Hyperbola and how is it calculated?

The latus rectum of Hyperbola denoted by 2l, is any of the chords parallel to the directrix and passing through a focus. It's half-length is the semi latus rectum and denoted by l. It is calculated by the formula 2l = 2b²/a where l is the semi-latus rectum of the hyperbola, b is the semi conjugate axis of the Hyperbola and a is the semi transverse axis of the Hyperbola.

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

Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis calculator uses Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1)) to calculate the Latus Rectum of Hyperbola, The Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola. Latus Rectum of Hyperbola is denoted by L symbol.

How to calculate Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis using this online calculator? To use this online calculator for Latus Rectum 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 Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis calculation can be explained with given input values -> 67.88225 = sqrt((2*12)^2*(3^2-1)).

FAQ

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

The Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola and is represented as L = sqrt((2*b)^2*(e^2-1)) or Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(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 Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis?

The Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola and is calculated using the eccentricity and semi-conjugate axis of the Hyperbola is calculated using Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1)). To calculate Latus Rectum 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 Latus Rectum of Hyperbola?

In this formula, Latus Rectum 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 -

Latus Rectum of Hyperbola = 2*(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola)
Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*(Eccentricity of Hyperbola^2-1)
Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*((Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola)^2-1)

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