Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Solution

STEP 0: Pre-Calculation Summary
Formula Used
Linear Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola
c = sqrt(1+L/(2*a))*a
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
Linear Eccentricity of Hyperbola - (Measured in Meter) - Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola.
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 Transverse Axis of Hyperbola - (Measured in Meter) - Semi Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.
STEP 1: Convert Input(s) to Base Unit
Latus Rectum of Hyperbola: 60 Meter --> 60 Meter No Conversion Required
Semi Transverse Axis of Hyperbola: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
c = sqrt(1+L/(2*a))*a --> sqrt(1+60/(2*5))*5
Evaluating ... ...
c = 13.228756555323
STEP 3: Convert Result to Output's Unit
13.228756555323 Meter --> No Conversion Required
FINAL ANSWER
13.228756555323 13.22876 Meter <-- Linear Eccentricity of Hyperbola
(Calculation completed in 00.020 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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6 Linear Eccentricity of Hyperbola Calculators

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

3 Linear Eccentricity of Hyperbola Calculators

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

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Formula

Linear Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola
c = sqrt(1+L/(2*a))*a

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 the Linear Eccentricity of Hyperbola and how it is calculated?

The linear eccentricity (c) is the distance between the center and a focus of the Hyperbola. Otherwise, linear eccentricity of Hyperbola is half of the distance between foci of the Hyperbola. It is calculated by the formula c = √((a2)+(b2)) where c is the linear eccentricity of the Hyperbola, a is the semi transverse axis of the Hyperbola and b is the semi conjugate axis of the Hyperbola.

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

Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis calculator uses Linear Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola to calculate the Linear Eccentricity of Hyperbola, The Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the latus rectum and semi-transverse axis of the Hyperbola. Linear Eccentricity of Hyperbola is denoted by c symbol.

How to calculate Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis using this online calculator? To use this online calculator for Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis, enter Latus Rectum of Hyperbola (L) & Semi Transverse Axis of Hyperbola (a) and hit the calculate button. Here is how the Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis calculation can be explained with given input values -> 13.22876 = sqrt(1+60/(2*5))*5.

FAQ

What is Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?
The Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the latus rectum and semi-transverse axis of the Hyperbola and is represented as c = sqrt(1+L/(2*a))*a or Linear Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola. 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 Transverse Axis of Hyperbola is half of the distance between the vertices of the Hyperbola.
How to calculate Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?
The Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as half of the distance between the foci of the Hyperbola and is calculated using the latus rectum and semi-transverse axis of the Hyperbola is calculated using Linear Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))*Semi Transverse Axis of Hyperbola. To calculate Linear Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis, you need Latus Rectum of Hyperbola (L) & Semi Transverse Axis of Hyperbola (a). With our tool, you need to enter the respective value for Latus Rectum of Hyperbola & Semi Transverse Axis 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 Linear Eccentricity of Hyperbola?
In this formula, Linear Eccentricity of Hyperbola uses Latus Rectum of Hyperbola & Semi Transverse Axis of Hyperbola. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Linear Eccentricity of Hyperbola = sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)
  • Linear Eccentricity of Hyperbola = Eccentricity of Hyperbola*Semi Transverse Axis of Hyperbola
  • Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity of Hyperbola^2))
  • Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2)))
  • Linear Eccentricity of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/Focal Parameter of Hyperbola
  • Linear Eccentricity of Hyperbola = sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)
  • Linear Eccentricity of Hyperbola = sqrt(Semi Conjugate Axis of Hyperbola^2/(1-1/Eccentricity of Hyperbola^2))
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