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: 2.66666Input: 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:
Ellipse
- Length of major axis is 2A.
- Length of minor axis is 2B.
- Therefore, the length of the latus rectum is:
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 ellipsedouble 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 Codeint 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 approachimport java.util.*;class GFG{// Function to calculate the length// of the latus rectum of an ellipsestatic 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 codepublic 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 ellipsedef 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 Codeif __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 approachusing 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 ellipsefunction 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 axisvar 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 Rectumdouble 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 inputsa1, b1 = 3, 2a2, b2 = 6, 3# Calculate the length of Latus Rectum for the first ellipsel1 = latus_rectum(a1, b1)# Display the result with formatted stringprint(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 ellipsel2 = latus_rectum(a2, b2)# Display the result with formatted stringprint(f"The length of the Latus Rectum of the ellipse with a = {a2} and b = {b2} is {l2:.5f}") |
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)
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