Área del cuadrado más grande que se puede inscribir en una elipse

Dada una elipse, con ejes mayores de longitud 2a y 2b , la tarea es encontrar el área del rectángulo más grande que se puede inscribir en ella.
Ejemplos: 
 

Input: a = 4, b = 2
Output: 1.25

Input: a = 5, b= 3
Output: 0.604444

Aproximación : Si un cuadrado está inscrito en una elipse, la distancia desde el centro del cuadrado a cualquiera de sus esquinas será igual a la distancia entre el origen y el punto en la esquina superior derecha en el diagrama a continuación, donde x=y
 

la ecuación de la elipse es x^2/a^2 + y^2/b^2 = 1 
Si, x = y 
entonces, x^2/a^2 + x^2/b^2 = 1 
entonces, x = √(a^2 + b^2)/ab 
so, y = √(a^2 + b^2)/ab 
So Área, A = 4(a^2 + b^2)/a^2b^2
 

A continuación se muestra la implementación del enfoque anterior:
 

// C++ Program to find the biggest square
// which can be inscribed within the ellipse
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of the square
float squarearea(float a, float b)
{
 
    // a and b cannot be negative
    if (a < 0 || b < 0)
        return -1;
 
    // area of the square
    float area = 4 * ((pow(a, 2) + pow(b, 2))
                      / (pow(a, 2) * pow(b, 2)));
 
    return area;
}
 
// Driver code
int main()
{
    float a = 4, b = 2;
    cout << squarearea(a, b) << endl;
 
    return 0;
}

// Java Program to find the biggest square
// which can be inscribed within the ellipse
import java.io.*;
 
class GFG {
 
 
// Function to find the area
// of the square
static float squarearea(float a, float b)
{
 
    // a and b cannot be negative
    if (a < 0 || b < 0)
        return -1;
 
    // area of the square
    float area = 4 *(float) ((Math.pow(a, 2) + Math.pow(b, 2))
                    / (Math.pow(a, 2) * Math.pow(b, 2)));
 
    return area;
}
 
// Driver code
 
    public static void main (String[] args) {
        float a = 4, b = 2;
    System.out.println( squarearea(a, b));
 
    }
}
// This code is contributed by inder_verma.

# Python3 Program to find the biggest square
# which can be inscribed within the ellipse
 
 
# Function to find the area
# of the square
def squarearea( a, b):
 
 
    # a and b cannot be negative
    if (a < 0 or b < 0):
        return -1
     
 
    # area of the square
    area = 4 * (((pow(a, 2) + pow(b, 2)) /
               (pow(a, 2) * pow(b, 2))))
 
    return area
 
 
# Driver code
if __name__=='__main__':
    a = 4
    b = 2
    print(squarearea(a, b))
 
# This code is contributed by ash264

// C# Program to find the biggest
// square which can be inscribed
// within the ellipse
using System;
 
class GFG
{
 
// Function to find the area
// of the square
static float squarearea(float a, float b)
{
 
    // a and b cannot be negative
    if (a < 0 || b < 0)
        return -1;
 
    // area of the square
    float area = 4 *(float) ((Math.Pow(a, 2) +
                              Math.Pow(b, 2)) /
                             (Math.Pow(a, 2) *
                              Math.Pow(b, 2)));
 
    return area;
}
 
// Driver code
public static void Main ()
{
    float a = 4, b = 2;
    Console.WriteLine( squarearea(a, b));
}
}
 
// This code is contributed by inder_verma

<?php
// PHP Program to find the biggest square
// which can be inscribed within the ellipse
 
 
// Function to find the area
// of the square
function squarearea( $a, $b)
{
 
    // a and b cannot be negative
    if ($a < 0 or $b < 0)
        return -1;
     
 
    // area of the square
    $area = 4 * (((pow($a, 2) + pow($b, 2)) /
            (pow($a, 2) * pow($b, 2))));
 
    return $area;
}
 
// Driver code
 
    $a = 4;
    $b = 2;
    print(squarearea($a, $b));
 
// This code is contributed by mits
?>

<script>
 
// javascript Program to find the biggest square
// which can be inscribed within the ellipse
 
// Function to find the area
// of the square
function squarearea(a , b)
{
 
    // a and b cannot be negative
    if (a < 0 || b < 0)
        return -1;
 
    // area of the square
    var area = 4 *((Math.pow(a, 2) + Math.pow(b, 2))
                    / (Math.pow(a, 2) * Math.pow(b, 2)));
 
    return area;
}
 
// Driver code
var a = 4, b = 2;
document.write( squarearea(a, b));
 
// This code contributed by shikhasingrajput
 
</script>

1.25

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