Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis Solution

STEP 0: Pre-Calculation Summary
Formula Used
Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*(Eccentricity of Hyperbola^2-1)
L = 2*a*(e^2-1)
This formula uses 3 Variables
Variables Used
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.
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
L = 2*a*(e^2-1) --> 2*5*(3^2-1)
Evaluating ... ...
L = 80
STEP 3: Convert Result to Output's Unit
80 Meter --> No Conversion Required
FINAL ANSWER
80 Meter <-- Latus Rectum of Hyperbola
(Calculation completed in 00.004 seconds)

Credits

Creator Image
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!
Verifier Image
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 1500+ more calculators!

Latus Rectum of Hyperbola Calculators

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

Latus Rectum of Hyperbola Calculators

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

Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis Formula

​LaTeX ​Go
Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*(Eccentricity of Hyperbola^2-1)
L = 2*a*(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 Latus Rectum of Hyperbola and how is it calculated?

The latus rectum of Hyperbola denoted by 2l, is any of the chords parallel to the directrix and passing through a focus. It's half-length is the semi latus rectum and denoted by l. It is calculated by the formula 2l = 2b2/a where l is the semi-latus rectum 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 Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis?

Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis calculator uses Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*(Eccentricity of Hyperbola^2-1) to calculate the Latus Rectum of Hyperbola, The Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis formula is defined as the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola and is calculated using the eccentricity and semi-transverse axis of the Hyperbola. Latus Rectum of Hyperbola is denoted by L symbol.

How to calculate Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis using this online calculator? To use this online calculator for Latus Rectum 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 Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis calculation can be explained with given input values -> 80 = 2*5*(3^2-1).

FAQ

What is Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis?
The Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis formula is defined as the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola and is calculated using the eccentricity and semi-transverse axis of the Hyperbola and is represented as L = 2*a*(e^2-1) or Latus Rectum of Hyperbola = 2*Semi Transverse Axis 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 Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis?
The Latus Rectum of Hyperbola given Eccentricity and Semi Transverse Axis formula is defined as the line segment passing through any of the foci and perpendicular to the transverse axis whose ends are on the Hyperbola and is calculated using the eccentricity and semi-transverse axis of the Hyperbola is calculated using Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*(Eccentricity of Hyperbola^2-1). To calculate Latus Rectum 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 Latus Rectum of Hyperbola?
In this formula, Latus Rectum of Hyperbola uses Semi Transverse Axis of Hyperbola & Eccentricity of Hyperbola. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Latus Rectum of Hyperbola = 2*(Semi Conjugate Axis of Hyperbola^2)/(Semi Transverse Axis of Hyperbola)
  • Latus Rectum of Hyperbola = sqrt((2*Semi Conjugate Axis of Hyperbola)^2*(Eccentricity of Hyperbola^2-1))
  • Latus Rectum of Hyperbola = 2*Semi Transverse Axis of Hyperbola*((Linear Eccentricity of Hyperbola/Semi Transverse Axis of Hyperbola)^2-1)
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!