Program to find the Eccentricity of a Hyperbola

Given two integers A and B, representing the length of the semi-major and semi-minor axis of a Hyperbola of the equation (X² / A²) – (Y² / B²) = 1, the task is to calculate the eccentricity of the given hyperbola.

Examples:

Input: A = 3, B = 2
Output: 1.20185
Explanation:
The eccentricity of the given hyperbola is 1.20185.

Input: A = 6, B = 3
Output: 1.11803

Approach: The given problem can be solved by using the formula to find the eccentricity of an ellipse.

• The length of the semi-major axis is A.
• The length of the semi-minor axis is B.
• Therefore, the eccentricity of the ellipse is given by  where A > B

Therefore, the idea is to print the value of  as the eccentricity of the ellipse.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the eccentricity
// of a hyperbola
double eccHyperbola(double A, double B)
{
    // Stores the squared ratio
    // of major axis to minor axis
    double r = (double)B * B / A * A;

    // Increment r by 1
    r += 1;

    // Return the square root of r
    return sqrt(r);
}

// Driver Code
int main()
{
    double A = 3.0, B = 2.0;
    cout << eccHyperbola(A, B);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;

class GFG{

// Function to find the eccentricity
// of a hyperbola
static double eccHyperbola(double A, double B)
{

    // Stores the squared ratio
    // of major axis to minor axis
    double r = (double)B * B / A * A;

    // Increment r by 1
    r += 1;

    // Return the square root of r
    return Math.sqrt(r);
}

// Driver Code
public static void main(String[] args)
{
    double A = 3.0, B = 2.0;

    System.out.print(eccHyperbola(A, B));
}
}

// This code is contributed by Amit Katiyar

Python3

# Python3 program for the above approach
import math

# Function to find the eccentricity
# of a hyperbola


def eccHyperbola(A, B):

    # Stores the squared ratio
    # of major axis to minor axis
    r = B * B / A * A

    # Increment r by 1
    r += 1

    # Return the square root of r
    return math.sqrt(r)


# Driver Code
if __name__ == "__main__":

    A = 3.0
    B = 2.0
    print(eccHyperbola(A, B))

    # This code is contributed by ukasp

C#

// C# program for the above approach
using System;

class GFG{

// Function to find the eccentricity
// of a hyperbola
static double eccHyperbola(double A, double B)
{

    // Stores the squared ratio
    // of major axis to minor axis
    double r = (double)B * B / A * A;

    // Increment r by 1
    r += 1;

    // Return the square root of r
    return Math.Sqrt(r);
}

// Driver Code
public static void Main(String[] args)
{
    double A = 3.0, B = 2.0;

    Console.Write(eccHyperbola(A, B));
}
}

// This code is contributed by Princi Singh

Javascript

<script>

// Javascript program for the above approach

// Function to find the eccentricity
// of a hyperbola
function eccHyperbola(A, B)
{

    // Stores the squared ratio
    // of major axis to minor axis
    let r = B * B / A * A;

    // Increment r by 1
    r += 1;

    // Return the square root of r
    return Math.sqrt(r);
}

// Driver Code
let A = 3.0;
let B = 2.0;

document.write(eccHyperbola(A, B));

// This code is contributed by mohit kumar

</script>

Output:

2.23607

Time Complexity: O(1)
Auxiliary Space: O(1)