给定截距的直线上距原点的法线长度

给定一条直线在两个轴上的截距为m和n 。任务是从原点找到这条直线上法线的长度。
例子：

Input: m = 5, n = 3 
Output: 2.57248
Input: m = 13, n = 9 
Output: 7.39973 
 

方法：线的法线是从垂直于给定线的点绘制的线段。

设p为从原点绘制到一条线的法线长度，该线与 x 轴的正方向对角θ ，如下所示。

然后，我们有cos Θ = p / m和sin Θ = p / n
因为， sin ² Θ + cos ² Θ = 1
所以， (p/m) ² + (p/n) ² = 1
我们得到， p = m * n / √(m ² + n ² )
下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
// Function to find the normal
// of the straight line
float normal(float m, float n)
{
    // Length of the normal
    float N = (fabsf(m) * fabsf(n))
              / sqrt((fabsf(m) * fabsf(m))
                     + (fabsf(n) * fabsf(n)));
 
    return N;
}
 
// Driver code
int main()
{
    float m = -5, n = 3;
    cout << normal(m, n);
 
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
 
// Function to find the normal
// of the straight line
static float normal(float m, float n)
{
    // Length of the normal
    float N = (float) ((Math.abs(m) * Math.abs(n))
            / Math.sqrt((Math.abs(m) * Math.abs(m))
                    + (Math.abs(n) * Math.abs(n))));
 
    return N;
}
 
// Driver code
public static void main(String[] args)
{
    float m = -5, n = 3;
    System.out.println(normal(m, n));
}
}
 
// This code has been contributed by 29AjayKumar

Python3

# Python3 implementation of the approach
import math;
 
# Function to find the normal
# of the straight line
def normal(m, n):
 
    # Length of the normal
    N = ((abs(m) * abs(n)) /
        math.sqrt((abs(m) * abs(m)) +
                  (abs(n) * abs(n))));
 
    return N;
 
# Driver code
m = -5; n = 3;
print(normal(m, n));
 
# This code is contributed
# by Akanksha Rai

C#

// C# implementation of the approach
using System;
 
class GFG
{
 
// Function to find the normal
// of the straight line
static float normal(float m, float n)
{
    // Length of the normal
    float N = (float)((Math.Abs(m) * Math.Abs(n)) /
                       Math.Sqrt((Math.Abs(m) * Math.Abs(m)) +
                                 (Math.Abs(n) * Math.Abs(n))));
 
    return N;
}
 
// Driver code
public static void Main()
{
    float m = -5, n = 3;
    Console.Write(normal(m, n));
}
}
 
// This code is contributed by Akanksha Rai

Javascript

 
// javascript implementation of the approach
 
 
// Function to find the normal
// of the straight line
function normal(m , n)
{
    // Length of the normal
    var N =  ((Math.abs(m) * Math.abs(n))
            / Math.sqrt((Math.abs(m) * Math.abs(m))
                    + (Math.abs(n) * Math.abs(n))));
 
    return N;
}
 
// Driver code
var m = -5, n = 3;
document.write(normal(m, n).toFixed(5));
 
// This code is contributed by Amit Katiyar
 

输出：

2.57248

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