求双曲线偏心率的程序

给定两个整数A和B ，代表方程(X ² / A ² ) – (Y ² / B ² ) = 1的双曲线的半长轴和半短轴的长度，任务是计算给定双曲线的偏心率。

例子：

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

方法：给定的问题可以通过使用公式来解决椭圆的偏心率。

• 半长轴的长度是A 。
• 半短轴的长度是B 。
• 因此，椭圆的偏心率由下式给出$\sqrt(1 + \frac{B^2}{A^2})$其中 A > B

因此，想法是打印的值$\sqrt(1 + \frac{B^2}{A^2})$作为椭圆的偏心率。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
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

 
// 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
 

输出：

2.23607

时间复杂度： O(1)
辅助空间： O(1)

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