Introduction to Latus Rectum Calculator:
Latus rectum Calculator is an online tool that helps you evaluate the length of the latus rectum for the given conic section area. It is used to find the line segment with the curve of the parabola, hyperbola, or ellipse.
The length of latus rectum of parabola calculator is a handy tool that can solve various types of conic section problems for different shapes and provide solutions of latus rectum length without taking any assistance from you except the input value only.
What is Latus Rectum?
Latus Rectum is a geometric term that is used to calculate the length of a line segment of different types of conic sections like hyperbola, parabola, and ellipse. It tells the behavior of geometric properties and dimensions of the conic section.
It is particularly useful in fields such as astronomy to explain the planetary orbit system or in engineering, and physics to understand the conic section area.
Formula of Latus Rectum:
The formula of latus rectum is vary as per the type of conic section you used for calculation. Here is the latus rectum formula for hyperbola, parabola, ellipse, etc. used by the endpoints of latus rectum calculator is,
For Parabola: y = 4ax2
Latus Rectum Lenth: 4a,
$$ For\; hyperbola: \frac{x^2}{a^2} - \frac{y^2}{b^2} \;=\; 1 $$
Latus Rectum Length: 2b2/a,
$$ For\; ellipse: \frac{x^2}{a^2} + \frac{y^2}{b^2} \;=\; 1 $$
How to Calculate Latus Rectum?
To calculate the length of the latus rectum from the conic section equation problem, the latus rectum of ellipse calculator calculates the base of the conic section like parabola, hyperbola, and ellipse properties for an accurate solution. Nevertheless, if you do not know we will tell you the right way about how to find the latus rectum.
Step 1:
Identify the given equation whether it is in a parabola, ellipse, or hyperbola, and identify its standard form for comparison.
Step 2:
While comparing the standard form and given function you need to get some values like for parabolas, find the value of a. For ellipses and hyperbola, find the value of a and b from the given equation.
Step 3:
Apply the formula for the latus rectum based on the type of conic section problem you have.
Step 4:
Add the values of a and b as per the required conic section in the formula of latus rectum to get the solution in the form of the length of the latus rectum.
Solved Example of Latus Rectum:
A solved example of the latus rectum gives you an idea about the working procedure of the length of latus rectum calculator with steps.
For parabola:
Example: Find the length of the latus rectum of the parabola,
$$ y^2 \;=\; 8x $$
Solution:
The equation of parabola is,
$$ y^2 \;=\; 4ax $$
As per the given value y2 = 8x. Compare the given value and the standard value of the parabola
$$ 4ax \;=\; 8x $$
$$ a \;=\; 2 $$
For latus rectum of parabola is y = 4a.
$$ Latus\; rectum\; =\; 4(2) \;=\; 8 $$
For ellipse:
Find the length of the latus rectum of the ellipse given by the equation,
$$ \frac{x^2}{25} + \frac{y^2}{16} \;=\; 1 $$
Solution:
The standard form of ellipse is,
$$ \frac{x^2}{a^2} + \frac{y^2}{b^2} \;=\; 1 $$
The given equation is,
$$ \frac{x^2}{25} + \frac{y^2}{16} \;=\; 1 $$
Compare both the equation
We get,
$$ a^2 \;=\; 25 $$
$$ b^2 \;=\; 16 $$
a = 5, b = 4 after taking the square root, the latus rectum formula is,
$$ Latus\; rectum\; for\; an\; ellipse\; =\; \frac{2b^2}{a} $$
Put the value in the latus rectum formula to get its length value,
$$ Latus\; rectum \;=\; 2(4)^{\frac{2}{5}} $$
$$ =\; \frac{32}{5} \;=\; 6.4 $$
For hyperbola:
Find the length of the latus rectum of the hyperbola given by the equation:
$$ \frac{x^2}{36} - \frac{y^2}{16} \;=\; 1 $$
Solution:
The standard form of hyperbola is,
$$ \frac{x^2}{a^2} - \frac{y^2}{b^2} \;=\; 1 $$
The given hyperbola equation is,
$$ \frac{x^2}{36} - \frac{y^2}{16} \;=\; 1 $$
Compare both the equations to get the value of a and b
$$ a^2 \;=\; 36\;and\; b^2 \;=\; 16 $$
$$ a \;=\; 6\; and\; b \;=\; 4 $$
The formula of latus rectum is,
$$ Latus\; rectum\; for\; a\; hyperbola\; =\; \frac{2b^2}{a} $$
$$ Latus\; rectum \;=\; 2(4)^{\frac{2}{6}} $$
$$ =\; \frac{32}{6} \;=\; 5.33 $$
Way to Use Latus Rectum Calculator:
The length of latus rectum of parabola calculator has a simple design, so you can use it to compute the given latus rectum of the conics section question solution. Before adding the input for the solutions of given conic section problems, you must follow some simple steps. These steps are:
- Choose the type of conic section from the given list.
- Enter the conic section problem to find the latus rectum in the input field.
- Recheck your input value for the latus rectum problem solution before hitting the calculate button to start the calculation process in the latus rectum of ellipse calculator.
- Click on the “Calculate” button to get the desired result of your given latus rectum problem.
- If you want to try out our latus rectum of hyperbola calculator to check its accuracy in solution, use the load example.
- Click on the “Recalculate” button to get a new page for solving more latus rectum questions.
Result from Latus Rectum of Parabola Calculator:
Length of Latus Rectum Calculator gives you the solution to a given latus rectum problem when you add the input value to it that may have:
- Result Option:
You can click on the result option as it provides you with a solution to the latus rectum for conic section questions.
- Possible Step:
When you click on the possible steps option it provides you with the solution of the conic section atus rectum problem in which steps are included.
Advantages of Using Latus Rectum of Ellipse Calculator:
The latus rectum of hyperbola calculator gives you multiple advantages whenever you use it to calculate the latus spectrum of conic section problems to get its solution. These advantages are:
- Our calculator saves the time and effort that you consume in solving latus rectum questions and getting solutions in a few seconds.
- It is a free-of-cost tool that provides you with a solution for a given conic section equation to find the latus rectum without paying a single penny.
- The latus rectum of parabola calculator ensures highly accurate results when computing conic section problems for the latus rectum with no errors that can occur in manual calculation methods.
- It is an adaptive tool that allows you to find the latus rectum of the conic section example.
- You can use this calculator for practice to get familiar with the latus rectum concept easily when you use it multiple times.
- Endpoints of latus rectum calculator is a trustworthy tool that provides you with correct solutions as per your input to calculate the latus rectum problem.
