Semi 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%

✖Semi Latus Rectum of Hyperbola is half of the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola.ⓘ Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis [L_Semi]

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Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Semi Latus Rectum of Hyperbola - (Measured in Meter) - Semi Latus Rectum of Hyperbola is half of 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_Semi = sqrt((2*b)^2*(e^2-1))/2 --> sqrt((2*12)^2*(3^2-1))/2

Evaluating ... ...

L_Semi = 33.9411254969543

STEP 3: Convert Result to Output's Unit

33.9411254969543 Meter --> No Conversion Required

FINAL ANSWER

33.9411254969543 ≈ 33.94113 Meter <-- Semi Latus Rectum of Hyperbola

(Calculation completed in 00.004 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)

Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis Formula

LaTeX Go

Semi Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))/2
L_Semi = sqrt((2*b)^2*(e^2-1))/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 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 Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis?

Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis calculator uses Semi Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))/2 to calculate the Semi Latus Rectum of Hyperbola, The Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as half of 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. Semi Latus Rectum of Hyperbola is denoted by L_Semi symbol.

How to calculate Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis using this online calculator? To use this online calculator for Semi 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 Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis calculation can be explained with given input values -> 33.94113 = sqrt((2*12)^2*(3^2-1))/2.

FAQ

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

The Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as half of 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_Semi = sqrt((2*b)^2*(e^2-1))/2 or Semi Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))/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 Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis?

The Semi Latus Rectum of Hyperbola given Eccentricity and Semi Conjugate Axis formula is defined as half of 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 Semi Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))/2. To calculate Semi 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 Semi Latus Rectum of Hyperbola?

In this formula, Semi 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 -

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

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