Program to find Length of Latus Rectum of an Ellipse
Last Updated :
23 Jul, 2025
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 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 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# 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.
<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>
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;
}
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
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}")
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
// 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)}`);
OutputThe 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)
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