Given here is a rectangle of length l & breadth b, the task is to find the area of the biggest ellipse that can be inscribed within it.
Examples:
Input: l = 5, b = 3 Output: 11.775 Input: 7, b = 4 Output: 21.98
Approach:
- Let, the length of the major axis of the ellipse = 2x and the length of the minor axis of the ellipse = 2y
- From the diagram, it is very clear that,
2x = l
2y = b
- So, Area of the ellipse = (? * x * y) = (? * l * b) / 4
Below is the implementation of the above approach:
C++
// C++ Program to find the biggest ellipse// which can be inscribed within the rectangle#include <bits/stdc++.h>using namespace std;// Function to find the area// of the ellipsefloat ellipse(float l, float b){ // The sides cannot be negative if (l < 0 || b < 0) return -1; // Area of the ellipse float x = (3.14 * l * b) / 4; return x;}// Driver codeint main(){ float l = 5, b = 3; cout << ellipse(l, b) << endl; return 0;} |
Java
// Java Program to find the biggest rectangle // which can be inscribed within the ellipse import java.util.*; import java.lang.*; import java.io.*; class GFG{ // Function to find the area // of the rectangle static float ellipse(float l, float b) { // a and b cannot be negative if (l < 0 || b < 0) return -1; float x = (float)(3.14 * l * b) / 4; return x; } // Driver code public static void main(String args[]) { float a = 5, b = 3; System.out.println(ellipse(a, b)); } } // This code is contributed// by Mohit Kumar |
Python3
# Python3 Program to find the biggest ellipse # which can be inscribed within the rectangle # Function to find the area# of the ellipse def ellipse(l, b): # The sides cannot be negative if l < 0 or b < 0: return -1 # Area of the ellipse x = (3.14 * l * b) / 4 return x # Driver code if __name__ == "__main__": l, b = 5, 3 print(ellipse(l, b)) # This code is contributed # by Rituraj Jain |
C#
// C# Program to find the biggest rectangle // which can be inscribed within the ellipse using System;class GFG{ // Function to find the area // of the rectangle static float ellipse(float l, float b) { // a and b cannot be negative if (l < 0 || b < 0) return -1; float x = (float)(3.14 * l * b) / 4; return x; } // Driver code public static void Main() { float a = 5, b = 3; Console.WriteLine(ellipse(a, b)); } } // This code is contributed// by Code_Mech. |
PHP
<?php// PHP Program to find the biggest ellipse// which can be inscribed within the rectangle// Function to find the area// of the ellipsefunction ellipse($l, $b){ // The sides cannot be negative if ($l < 0 || $b < 0) return -1; // Area of the ellipse $x = (3.14 * $l * $b) / 4; return $x;}// Driver code$l = 5; $b = 3;echo ellipse($l, $b) . "\n";// This code is contributed// by Akanksha Rai?> |
Javascript
<script>// javascript Program to find the biggest rectangle // which can be inscribed within the ellipse // Function to find the area // of the rectangle function ellipse(l , b) { // a and b cannot be negative if (l < 0 || b < 0) return -1; var x = (3.14 * l * b) / 4; return x; } // Driver code var a = 5, b = 3; document.write(ellipse(a, b)); // This code is contributed by Amit Katiyar </script> |
Output:
11.775
Time Complexity: O(1)
Auxiliary Space: O(1)
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