Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis Solution

STEP 0: Pre-Calculation Summary
Formula Used
Focal Parameter of Hyperbola = Semi Transverse Axis of Hyperbola/Eccentricity of Hyperbola*(Eccentricity of Hyperbola^2-1)
p = a/e*(e^2-1)
This formula uses 3 Variables
Variables Used
Focal Parameter of Hyperbola - (Measured in Meter) - Focal Parameter of Hyperbola is the shortest distance between any of the foci and directrix of the corresponding wing of 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.
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 Transverse Axis of Hyperbola: 5 Meter --> 5 Meter No Conversion Required
Eccentricity of Hyperbola: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
p = a/e*(e^2-1) --> 5/3*(3^2-1)
Evaluating ... ...
p = 13.3333333333333
STEP 3: Convert Result to Output's Unit
13.3333333333333 Meter --> No Conversion Required
FINAL ANSWER
13.3333333333333 13.33333 Meter <-- Focal Parameter of Hyperbola
(Calculation completed in 00.004 seconds)

Credits

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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8 Focal Parameter of Hyperbola Calculators

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

4 Focal Parameter of Hyperbola Calculators

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

Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis Formula

Focal Parameter of Hyperbola = Semi Transverse Axis of Hyperbola/Eccentricity of Hyperbola*(Eccentricity of Hyperbola^2-1)
p = a/e*(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 Focal Parameter of a Hyperbola and how is it calculated?

The focal parameter of the Hyperbola is the shortest distance from a focus to the corresponding directrix. It is calculated by the formula p= b2/√(a2+b2) where p is the focal parameter 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 Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis?

Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis calculator uses Focal Parameter of Hyperbola = Semi Transverse Axis of Hyperbola/Eccentricity of Hyperbola*(Eccentricity of Hyperbola^2-1) to calculate the Focal Parameter of Hyperbola, The Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis formula is defined as the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola and is calculated using the eccentricity and semi-transverse axis of the Hyperbola. Focal Parameter of Hyperbola is denoted by p symbol.

How to calculate Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis using this online calculator? To use this online calculator for Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis, enter Semi Transverse Axis of Hyperbola (a) & Eccentricity of Hyperbola (e) and hit the calculate button. Here is how the Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis calculation can be explained with given input values -> 13.33333 = 5/3*(3^2-1).

FAQ

What is Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis?
The Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis formula is defined as the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola and is calculated using the eccentricity and semi-transverse axis of the Hyperbola and is represented as p = a/e*(e^2-1) or Focal Parameter of Hyperbola = Semi Transverse Axis of Hyperbola/Eccentricity of Hyperbola*(Eccentricity of Hyperbola^2-1). Semi Transverse Axis of Hyperbola is half of the distance between the vertices 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 Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis?
The Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis formula is defined as the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola and is calculated using the eccentricity and semi-transverse axis of the Hyperbola is calculated using Focal Parameter of Hyperbola = Semi Transverse Axis of Hyperbola/Eccentricity of Hyperbola*(Eccentricity of Hyperbola^2-1). To calculate Focal Parameter of Hyperbola given Eccentricity and Semi Transverse Axis, you need Semi Transverse Axis of Hyperbola (a) & Eccentricity of Hyperbola (e). With our tool, you need to enter the respective value for Semi Transverse 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 Focal Parameter of Hyperbola?
In this formula, Focal Parameter of Hyperbola uses Semi Transverse Axis of Hyperbola & Eccentricity of Hyperbola. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)
  • Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola
  • Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola/(Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1))
  • Focal Parameter of Hyperbola = (Linear Eccentricity of Hyperbola^2-Semi Transverse Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola
  • Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola^2/(Semi Transverse Axis of Hyperbola*Eccentricity of Hyperbola)
  • Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola^2/sqrt(((2*Semi Conjugate Axis of Hyperbola^2)/Latus Rectum of Hyperbola)^2+Semi Conjugate Axis of Hyperbola^2)
  • Focal Parameter of Hyperbola = ((Semi Transverse Axis of Hyperbola*Latus Rectum of Hyperbola)/2)/sqrt(Semi Transverse Axis of Hyperbola^2+((Semi Transverse Axis of Hyperbola*Latus Rectum of Hyperbola)/2)^2)
  • Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/sqrt(Semi Transverse Axis of Hyperbola^2+Semi Conjugate Axis of Hyperbola^2)
  • Focal Parameter of Hyperbola = Semi Conjugate Axis of Hyperbola^2/sqrt(((2*Semi Conjugate Axis of Hyperbola^2)/Latus Rectum of Hyperbola)^2+Semi Conjugate Axis of Hyperbola^2)
  • Focal Parameter of Hyperbola = (Semi Conjugate Axis of Hyperbola^2)/Linear Eccentricity of Hyperbola
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