# Perimeter of an Ellipse

An ellipse is described as a curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. Ellipse has two types of axis – Major Axis and Minor Axis. The longest chord of the ellipse is the major axis. The perpendicular chord to the major axis is the minor axis which bisects the major axis at the center.

Given the lengths of minor and major axis of an ellipse, the task is to find the perimeter of the Ellipse.

**Examples:**

Input:a = 3, b = 2

Output:16.0109

Input:a = 9, b = 5

Output:45.7191

**Perimeter of an ellipse is**:

Perimeter : 2π * sqrt( (a

^{2}+ b^{2}) / 2 )

Where a and b are semi-major axis and semi-minor axis respectively.

Below is the implementation of the above approach:

## C++

`// C++ program to find perimeter of an Ellipse ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the perimeter of an Ellipse ` `void` `Perimeter(` `int` `a, ` `int` `b) ` `{ ` ` ` `float` `perimeter; ` ` ` ` ` `// Compute perimeter ` ` ` `perimeter = 2 * 3.14 * ` `sqrt` `((a * a + b * b) / (2 * 1.0)); ` ` ` ` ` `cout << perimeter; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `a = 3, b = 2; ` ` ` ` ` `// Function call ` ` ` `Perimeter(a, b); ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find perimeter of ` `// an Ellipse. ` `import` `java.lang.Math; ` `class` `GFG1{ ` ` ` ` ` `// Function to find perimeter of an ` ` ` `// ellipse. ` ` ` `static` `void` `Perimeter( ` `double` `a, ` `double` `b) ` ` ` `{ ` ` ` `double` `Perimeter; ` ` ` ` ` `// formula to find the Perimeter ` ` ` `// of an Ellipse. ` ` ` `Perimeter = (` `double` `)` `2` `* ` `3.14` `* Math.sqrt((a * a + b * b) / (` `2` `* ` `1.0` `)) ; ` ` ` ` ` `// Display the result ` ` ` `System.out.println(` `"Perimeter: "` `+ Perimeter); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main (String[] args) ` ` ` `{ ` ` ` `double` `a = ` `3` `, b = ` `2` `; ` ` ` ` ` `Perimeter(a , b); ` ` ` `} ` `} ` |

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## Python3

`# Python3 program to find perimeter ` `# of an Ellipse ` `from` `math ` `import` `sqrt ` ` ` `# Function to find the perimeter ` `# of an Ellipse ` `def` `Perimeter(a, b): ` ` ` `permeter ` `=` `0` ` ` ` ` `# Compute perimeter ` ` ` `permeter ` `=` `(` `2` `*` `3.14` `*` ` ` `sqrt((a ` `*` `a ` `+` `b ` `*` `b) ` `/` ` ` `(` `2` `*` `1.0` `))); ` ` ` ` ` `print` `(permeter) ` ` ` `# Driver code ` `a ` `=` `3` `b ` `=` `2` ` ` `# Function call ` `Perimeter(a, b) ` ` ` `# This code is contributed ` `# by Mohit Kumar ` |

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## C#

// C# program to find perimeter of

// an Ellipse.

using System;

class GFG1

{

// Function to find perimeter of an

// ellipse.

static void Perimeter(double a, double b)

{

double Perimeter;

// formula to find the Perimeter

// of an Ellipse.

Perimeter = (double)2 * 3.14 *

Math.Sqrt((a * a + b * b) / (2 * 1.0));

// Display the result

Console.WriteLine(“Perimeter: ” + Perimeter);

}

// Driver code

public static void Main (String[] args)

{

double a = 3, b = 2;

Perimeter(a , b);

}

}

// This code is contributed by Princi Singh

**Output :**

16.010921272681344

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