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:
- 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++ 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> |
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.
#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)}`);
|
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)