Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Solution

STEP 0: Pre-Calculation Summary
Formula Used
Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))
e = sqrt(1+L/(2*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
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.
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
e = sqrt(1+L/(2*a)) --> sqrt(1+60/(2*5))
Evaluating ... ...
e = 2.64575131106459
STEP 3: Convert Result to Output's Unit
2.64575131106459 Meter --> No Conversion Required
FINAL ANSWER
2.64575131106459 2.645751 Meter <-- Eccentricity of Hyperbola
(Calculation completed in 00.006 seconds)

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

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

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis Formula

Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))
e = sqrt(1+L/(2*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 Eccentricity of the Hyperbola and how is it calculated?

The eccentricity of a Hyperbola is the ratio of the distances from any point on the Hyperbola to the focus and the corresponding directrix. It is calculated by the formula e = c/a where e is the eccentricity of the Hyperbola, c is the linear eccentricity of the Hyperbola and a is the semi-transverse of the Hyperbola.

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

Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis calculator uses Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola)) to calculate the Eccentricity of Hyperbola, The Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, and is calculated using the latus rectum and semi-transverse axis of the Hyperbola. Eccentricity of Hyperbola is denoted by e symbol.

How to calculate Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis using this online calculator? To use this online calculator for 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 Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis calculation can be explained with given input values -> 2.645751 = sqrt(1+60/(2*5)).

FAQ

What is Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?
The Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, and is calculated using the latus rectum and semi-transverse axis of the Hyperbola and is represented as e = sqrt(1+L/(2*a)) or Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*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 Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis?
The Eccentricity of Hyperbola given Latus Rectum and Semi Transverse Axis formula is defined as the ratio of distances of any point on the Hyperbola from focus and the directrix, and is calculated using the latus rectum and semi-transverse axis of the Hyperbola is calculated using Eccentricity of Hyperbola = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola)). To calculate 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 Eccentricity of Hyperbola?
In this formula, Eccentricity of Hyperbola uses Latus Rectum of Hyperbola & Semi Transverse Axis of Hyperbola. We can use 6 other way(s) to calculate the same, which is/are as follows -
  • Eccentricity of Hyperbola = sqrt(1+(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola^2))
  • Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola
  • Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2)
  • Eccentricity of Hyperbola = sqrt(1+(Latus Rectum of Hyperbola)^2/(2*Semi Conjugate Axis of Hyperbola)^2)
  • Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola^2/(Semi Transverse Axis of Hyperbola*Focal Parameter of Hyperbola)
  • Eccentricity of Hyperbola = Semi Conjugate Axis of Hyperbola/sqrt(Semi Conjugate Axis of Hyperbola^2-Focal Parameter of Hyperbola^2)
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