Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Semi Conjugate Axis of Hyperbola = (Latus Rectum of Hyperbola*Focal Parameter of Hyperbola)/sqrt(Latus Rectum of Hyperbola^2-(2*Focal Parameter of Hyperbola)^2)
b = (L*p)/sqrt(L^2-(2*p)^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 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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Latus Rectum of Hyperbola: 60 Meter --> 60 Meter No Conversion Required
Focal Parameter of Hyperbola: 11 Meter --> 11 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
b = (L*p)/sqrt(L^2-(2*p)^2) --> (60*11)/sqrt(60^2-(2*11)^2)
Evaluating ... ...
b = 11.8234770043503
STEP 3: Convert Result to Output's Unit
11.8234770043503 Meter --> No Conversion Required
FINAL ANSWER
11.8234770043503 11.82348 Meter <-- Semi Conjugate Axis of Hyperbola
(Calculation completed in 00.020 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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12 Conjugate Axis of Hyperbola Calculators

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

Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter Formula

Semi Conjugate Axis of Hyperbola = (Latus Rectum of Hyperbola*Focal Parameter of Hyperbola)/sqrt(Latus Rectum of Hyperbola^2-(2*Focal Parameter of Hyperbola)^2)
b = (L*p)/sqrt(L^2-(2*p)^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 Conjugate Axis of the Hyperbola and how is it calculated?

The conjugate axis of Hyperbola is the line perpendicular to the transverse axis and has the co-vertices as its endpoints. It is calculated by the equation c = 2b where c is the length of the conjugate axis of the Hyperbola and b is the semi conjugate axis of the Hyperbola.

How to Calculate Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter?

Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter calculator uses Semi Conjugate Axis of Hyperbola = (Latus Rectum of Hyperbola*Focal Parameter of Hyperbola)/sqrt(Latus Rectum of Hyperbola^2-(2*Focal Parameter of Hyperbola)^2) to calculate the Semi Conjugate Axis of Hyperbola, The Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter formula is defined as 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, and is calculated using the latus rectum and the focal parameter of the Hyperbola. Semi Conjugate Axis of Hyperbola is denoted by b symbol.

How to calculate Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter using this online calculator? To use this online calculator for Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter, enter Latus Rectum of Hyperbola (L) & Focal Parameter of Hyperbola (p) and hit the calculate button. Here is how the Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter calculation can be explained with given input values -> 11.82348 = (60*11)/sqrt(60^2-(2*11)^2).

FAQ

What is Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter?
The Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter formula is defined as 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, and is calculated using the latus rectum and the focal parameter of the Hyperbola and is represented as b = (L*p)/sqrt(L^2-(2*p)^2) or Semi Conjugate Axis of Hyperbola = (Latus Rectum of Hyperbola*Focal Parameter of Hyperbola)/sqrt(Latus Rectum of Hyperbola^2-(2*Focal Parameter of Hyperbola)^2). 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 & Focal Parameter of Hyperbola is the shortest distance between any of the foci and directrix of the corresponding wing of the Hyperbola.
How to calculate Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter?
The Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter formula is defined as 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, and is calculated using the latus rectum and the focal parameter of the Hyperbola is calculated using Semi Conjugate Axis of Hyperbola = (Latus Rectum of Hyperbola*Focal Parameter of Hyperbola)/sqrt(Latus Rectum of Hyperbola^2-(2*Focal Parameter of Hyperbola)^2). To calculate Semi Conjugate Axis of Hyperbola given Latus Rectum and Focal Parameter, you need Latus Rectum of Hyperbola (L) & Focal Parameter of Hyperbola (p). With our tool, you need to enter the respective value for Latus Rectum of Hyperbola & Focal Parameter 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 Conjugate Axis of Hyperbola?
In this formula, Semi Conjugate Axis of Hyperbola uses Latus Rectum of Hyperbola & Focal Parameter of Hyperbola. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Semi Conjugate Axis of Hyperbola = Semi Transverse Axis of Hyperbola*sqrt(Eccentricity of Hyperbola^2-1)
  • Semi Conjugate Axis of Hyperbola = sqrt((Latus Rectum of Hyperbola)^2/(Eccentricity of Hyperbola^2-1))/2
  • Semi Conjugate Axis of Hyperbola = Linear Eccentricity of Hyperbola*sqrt(1-1/Eccentricity of Hyperbola^2)
  • Semi Conjugate Axis of Hyperbola = Conjugate Axis of Hyperbola/2
  • Semi Conjugate Axis of Hyperbola = sqrt((Latus Rectum of Hyperbola*Semi Transverse Axis of Hyperbola)/2)
  • Semi Conjugate Axis of Hyperbola = sqrt(Linear Eccentricity of Hyperbola^2-Semi Transverse Axis of Hyperbola^2)
  • Semi Conjugate Axis of Hyperbola = (Eccentricity of Hyperbola/sqrt(Eccentricity of Hyperbola^2-1))*Focal Parameter of Hyperbola
  • Semi Conjugate Axis of Hyperbola = sqrt(Focal Parameter of Hyperbola*Linear Eccentricity of Hyperbola)
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