Area of the biggest ellipse inscribed within a rectangle

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: 

1. Let, the length of the major axis of the ellipse = 2x and the length of the minor axis of the ellipse = 2y
2. From the diagram, it is very clear that, 
   2x = l 
   2y = b
   
3. So, Area of the ellipse = (π * x * y) = (π * 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 ellipse
float 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 code
int 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 ellipse
function 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)