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 hyperboladouble 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 Codeint main(){ double A = 3.0, B = 2.0; cout << eccHyperbola(A, B); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{// Function to find the eccentricity// of a hyperbolastatic 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 Codepublic 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 approachimport math# Function to find the eccentricity# of a hyperboladef 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 Codeif __name__ == "__main__": A = 3.0 B = 2.0 print(eccHyperbola(A, B)) # This code is contributed by ukasp |
C#
// C# program for the above approachusing System;class GFG{// Function to find the eccentricity// of a hyperbolastatic 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 Codepublic 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 hyperbolafunction 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 Codelet 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)
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