可以刻在椭圆上的最大正方形的面积

给定一个椭圆，主轴长度为2a和2b ，任务是找到可以在其中刻出的最大矩形区域。
例子：

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

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

方法：如果将正方形内接在椭圆上，则从正方形的中心到其任何一个角的距离将等于下图中右上角的原点和点之间的距离，其中x = y

the equation of the ellipse is x^2/a^2 + y^2/b^2 = 1 
If, x = y 
then, x^2/a^2 + x^2/b^2 = 1 
therefore, x = √(a^2 + b^2)/ab 
so, y = √(a^2 + b^2)/ab 
So Area, A = 4(a^2 + b^2)/a^2b^2
 

下面是上述方法的实现：

C++

// C++ Program to find the biggest square
// which can be inscribed within the ellipse
#include 
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

// 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.

Python 3

# 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#

// 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

Javascript

 
// 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
 

输出：

1.25