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Program to find Length of Latus Rectum of an Ellipse

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Given two integers A and B, representing the length of semi-major and semi-minor axis of an Ellipse with general equation (x2 / A2) + (y2 / B2) = 1, the task is to find the length of the latus rectum of the ellipse

Examples:

Input: A = 3, B = 2
Output: 2.66666

Input: A = 6, B = 3
Output: 3

Approach: The given problem can be solved based on the following observations: 

  • The Latus Rectum of an Ellipse is the focal chord perpendicular to the major axis whose length is equal to:
     \frac{(length\ of\  minor\ axis)^2}{(length\ of\ major\ axis)}

Ellipse

  • Length of major axis is 2A.
  • Length of minor axis is 2B.
  • Therefore, the length of the latus rectum is:
     d_{LL'}=2\frac{B^2}{A}

Follow the steps below to solve the given problem:

  • Initialize two variables, say major and minor, to store the length of the major-axis (= 2A) and the length of the minor-axis (= 2B) of the Ellipse respectively.
  • Calculate the square of minor and divide it with major. Store the result in a double variable, say latus_rectum.
  • Print the value of latus_rectum as the final result. 

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <iostream>
using namespace std;
 
// Function to calculate the length
// of the latus rectum of an ellipse
double lengthOfLatusRectum(double A,
                           double B)
{
    // Length of major axis
    double major = 2.0 * A;
   
    // Length of minor axis
    double minor = 2.0 * B;
   
    // Length of the latus rectum
    double latus_rectum = (minor*minor)/major;
   
    return latus_rectum;
}
 
// Driver Code
int main()
{
    // Given lengths of semi-major
  // and semi-minor axis
    double A = 3.0, B = 2.0;
   
    // Function call to calculate length
    // of the latus rectum of a ellipse
    cout << lengthOfLatusRectum(A, B);
    return 0;
}

                    

Java

// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to calculate the length
// of the latus rectum of an ellipse
static double lengthOfLatusRectum(double A,
                                  double B)
{
     
    // Length of major axis
    double major = 2.0 * A;
     
    // Length of minor axis
    double minor = 2.0 * B;
     
    // Length of the latus rectum
    double latus_rectum = (minor * minor) / major;
     
    return latus_rectum;
}
 
// Driver code
public static void main(String[] args)
{
     
    // Given lengths of semi-major
    // and semi-minor axis
    double A = 3.0, B = 2.0;
 
    // Function call to calculate length
    // of the latus rectum of a ellipse
    System.out.print(lengthOfLatusRectum(A, B));
}
}
 
// This code is contributed by susmitakundugoaldanga

                    

Python3

# Python3 program for the above approach
 
# Function to calculate the length
# of the latus rectum of an ellipse
def lengthOfLatusRectum(A, B):
   
    # Length of major axis
    major = 2.0 * A
 
    # Length of minor axis
    minor = 2.0 * B
 
    # Length of the latus rectum
    latus_rectum = (minor*minor)/major
    return latus_rectum
 
# Driver Code
if __name__ == "__main__":
 
    # Given lengths of semi-major
        # and semi-minor axis
    A = 3.0
    B = 2.0
 
    # Function call to calculate length
    # of the latus rectum of a ellipse
    print('%.5f' % lengthOfLatusRectum(A, B))
 
    # This code is contributed by ukasp.

                    

C#

// C# program for the above approach
using System;
 
class GFG
{
 
  // Function to calculate the length
  // of the latus rectum of an ellipse
  static double lengthOfLatusRectum(double A,
                                    double B)
  {
    // Length of major axis
    double major = 2.0 * A;
 
    // Length of minor axis
    double minor = 2.0 * B;
 
    // Length of the latus rectum
    double latus_rectum = (minor*minor)/major;
 
    return latus_rectum;
  }
 
  // Driver Code
  public static void Main()
  {
 
    // Given lengths of semi-major
    // and semi-minor axis
    double A = 3.0, B = 2.0;
 
    // Function call to calculate length
    // of the latus rectum of a ellipse
    Console.WriteLine(lengthOfLatusRectum(A, B));
  }
}
 
// This code is contributed by souravghosh0416.

                    

Javascript

<script>
 
// Javascript program for the above approach
 
// Function to calculate the length
// of the latus rectum of an ellipse
function lengthOfLatusRectum(A, B)
{
     
    // Length of major axis
    var major = 2.0 * A;
     
    // Length of minor axis
    var minor = 2.0 * B;
     
    // Length of the latus rectum
    var latus_rectum = (minor * minor) / major;
     
    return latus_rectum;
}
 
// Driver code
 
// Given lengths of semi-major
// and semi-minor axis
var A = 3.0, B = 2.0;
 
document.write(lengthOfLatusRectum(A, B));
 
// This code is contributed by Ankita saini
    
</script>

                    

Output
2.66667






Time Complexity: O(1)
Auxiliary Space: O(1) 

Using the formula :

Approach:

The length of the Latus Rectum of an Ellipse can be calculated using the formula: L = 2b^2/a, where a and b are the lengths of the major and minor axis of the ellipse, respectively.

Define a function latus_rectum that takes two arguments a and b.
Inside the function, calculate the length of the Latus Rectum using the formula 2 * b ** 2 / a and return the result.
Call the function twice with different values of a and b.
Print the results using formatted strings to display the inputs and outputs with appropriate decimal places.

C++

#include <iostream>
#include <iomanip> // For setting the precision of the output
 
// Function to calculate the length of Latus Rectum
double latusRectum(double a, double b) {
    return (2 * b * b) / a;
}
 
int main() {
    // Example inputs
    double a1 = 3, b1 = 2;
    double a2 = 6, b2 = 3;
 
    // Calculate the length of Latus Rectum for the first ellipse
    double l1 = latusRectum(a1, b1);
 
    // Display the result with formatted string
    std::cout << "The length of the Latus Rectum of the ellipse with a = "
         << a1 << " and b = " << b1
              << " is " << std::fixed << std::setprecision(5) << l1 << std::endl;
 
    // Calculate the length of Latus Rectum for the second ellipse
    double l2 = latusRectum(a2, b2);
 
    // Display the result with formatted string
    std::cout << "The length of the Latus Rectum of the ellipse with a = "
              << a2 << " and b = " << b2
              << " is " << std::fixed << std::setprecision(5) << l2 << std::endl;
 
    return 0;
}

                    

Java

public class Main {
    // Function to calculate the length of Latus Rectum
    static double latusRectum(double a, double b) {
        return (2 * b * b) / a;
    }
 
    public static void main(String[] args) {
        // Example inputs
        double a1 = 3, b1 = 2;
        double a2 = 6, b2 = 3;
 
        // Calculate the length of Latus Rectum for the first ellipse
        double l1 = latusRectum(a1, b1);
 
        // Display the result with formatted string
        System.out.println("The length of the Latus Rectum of the ellipse with a = " + a1 +
                " and b = " + b1 + " is " + String.format("%.5f", l1));
 
        // Calculate the length of Latus Rectum for the second ellipse
        double l2 = latusRectum(a2, b2);
 
        // Display the result with formatted string
        System.out.println("The length of the Latus Rectum of the ellipse with a = " + a2 +
                " and b = " + b2 + " is " + String.format("%.5f", l2));
    }
}
 
// This code is contributed by shivamgupta0987654321

                    

Python3

def latus_rectum(a, b):
    return 2 * b ** 2 / a
 
# Example inputs
a1, b1 = 3, 2
a2, b2 = 6, 3
 
# Calculate the length of Latus Rectum for the first ellipse
l1 = latus_rectum(a1, b1)
 
# Display the result with formatted string
print(f"The length of the Latus Rectum of the ellipse with a = {a1} and b = {b1} is {l1:.5f}")
 
# Calculate the length of Latus Rectum for the second ellipse
l2 = latus_rectum(a2, b2)
 
# Display the result with formatted string
print(f"The length of the Latus Rectum of the ellipse with a = {a2} and b = {b2} is {l2:.5f}")

                    

C#

using System;
 
class Program
{
    // Function to calculate the length of Latus Rectum
    static double LatusRectum(double a, double b)
    {
        return (2 * b * b) / a;
    }
 
    static void Main()
    {
        // Example inputs
        double a1 = 3, b1 = 2;
        double a2 = 6, b2 = 3;
 
        // Calculate the length of Latus Rectum for the first ellipse
        double l1 = LatusRectum(a1, b1);
 
        // Display the result with formatted string
        Console.WriteLine($"The length of the Latus Rectum of the ellipse with a = {a1} and b = {b1} is {l1:F5}");
 
        // Calculate the length of Latus Rectum for the second ellipse
        double l2 = LatusRectum(a2, b2);
 
        // Display the result with formatted string
        Console.WriteLine($"The length of the Latus Rectum of the ellipse with a = {a2} and b = {b2} is {l2:F5}");
    }
}
// This code is contributed by shivamgupta310570

                    

Javascript

// Function to calculate the length of Latus Rectum
function latusRectum(a, b) {
    return (2 * b * b) / a;
}
 
// Example inputs
let a1 = 3, b1 = 2;
let a2 = 6, b2 = 3;
 
// Calculate the length of Latus Rectum for the first ellipse
let l1 = latusRectum(a1, b1);
 
// Display the result with formatted string
console.log(`The length of the Latus Rectum of the ellipse with a = ${a1} and b = ${b1} is ${l1.toFixed(5)}`);
 
// Calculate the length of Latus Rectum for the second ellipse
let l2 = latusRectum(a2, b2);
 
// Display the result with formatted string
console.log(`The length of the Latus Rectum of the ellipse with a = ${a2} and b = ${b2} is ${l2.toFixed(5)}`);

                    

Output
The length of the Latus Rectum of the ellipse with a = 3 and b = 2 is 2.66667
The length of the Latus Rectum of the ellipse with a = 6 and b = 3 is 3.00000






Time complexity: O(1)
Auxiliary Space: O(1)



Last Updated : 04 Dec, 2023
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