Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis Calculator

✖Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola.ⓘ Linear Eccentricity of Hyperbola [c]			+10% -10%
✖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 given Linear Eccentricity and Semi Conjugate Axis [e]

⎘ Copy

👎

Formula

✖

Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis

Formula

`"e" = "c"/sqrt("c"^2-"b"^2)`

Example

`"2.6m"="13m"/sqrt(("13m")^2-("12m")^2)`

Calculator

LaTeX

Reset

👍

Download Hyperbola Formula PDF PDF Image

Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis Solution

STEP 0: Pre-Calculation Summary

Formula Used

Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2)
e = c/sqrt(c^2-b^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

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.
Linear Eccentricity of Hyperbola - (Measured in Meter) - Linear Eccentricity of Hyperbola is half of the distance between foci of 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.

STEP 1: Convert Input(s) to Base Unit

Linear Eccentricity of Hyperbola: 13 Meter --> 13 Meter No Conversion Required
Semi Conjugate Axis of Hyperbola: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e = c/sqrt(c^2-b^2) --> 13/sqrt(13^2-12^2)

Evaluating ... ...

e = 2.6

STEP 3: Convert Result to Output's Unit

2.6 Meter --> No Conversion Required

FINAL ANSWER

2.6 Meter <-- Eccentricity of Hyperbola

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 2D Geometry » Hyperbola » Eccentricity of Hyperbola » Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis

Credits

Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

Dhruv Walia has created this Calculator and 1100+ more calculators!

Verified by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has verified this Calculator and 1400+ more calculators!

< 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 Linear Eccentricity and Semi Conjugate Axis Formula

Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2)
e = c/sqrt(c^2-b^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 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 Linear Eccentricity and Semi Conjugate Axis?

Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis calculator uses Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2) to calculate the Eccentricity of Hyperbola, The Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate 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 linear eccentricity and semi conjugate axis of the Hyperbola. Eccentricity of Hyperbola is denoted by e symbol.

How to calculate Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis using this online calculator? To use this online calculator for Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis, enter Linear Eccentricity of Hyperbola (c) & Semi Conjugate Axis of Hyperbola (b) and hit the calculate button. Here is how the Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis calculation can be explained with given input values -> 2.6 = 13/sqrt(13^2-12^2).

FAQ

What is Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis?

The Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate 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 linear eccentricity and semi conjugate axis of the Hyperbola and is represented as e = c/sqrt(c^2-b^2) or Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2). Linear Eccentricity of Hyperbola is half of the distance between foci of the Hyperbola & 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.

How to calculate Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis?

The Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate 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 linear eccentricity and semi conjugate axis of the Hyperbola is calculated using Eccentricity of Hyperbola = Linear Eccentricity of Hyperbola/sqrt(Linear Eccentricity of Hyperbola^2-Semi Conjugate Axis of Hyperbola^2). To calculate Eccentricity of Hyperbola given Linear Eccentricity and Semi Conjugate Axis, you need Linear Eccentricity of Hyperbola (c) & Semi Conjugate Axis of Hyperbola (b). With our tool, you need to enter the respective value for Linear Eccentricity of Hyperbola & Semi Conjugate 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 Linear Eccentricity of Hyperbola & Semi Conjugate 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 = sqrt(1+Latus Rectum of Hyperbola/(2*Semi Transverse Axis of Hyperbola))
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)

Home

FREE PDFs

🔍 Search