穿过给定点的直线方程，将其等分为两个相等的线段

给定一条直线通过给定点(x ₀ ，y ₀ ) ，以使该点将线段一分为二。任务是找到这条直线的方程式。
例子：

Input: x₀ = 4, y₀ = 3 
Output: 3x + 4y = 24
Input: x₀ = 7, y₀ = 12 
Output: 12x + 7y = 168 
 

方法：

令PQ为直线， AB为轴之间的线段。 x截距和y截距分别为a和b 。
现在，由于C(x ₀ ，y ₀ )将AB对等，
x ₀ =(a + 0)/ 2，即a = 2x ₀
类似地， y ₀ =(0 + b)/ 2即b = 2y ₀
我们知道intecept形式的直线方程为

x / a + y / b = 1 
Here, a = 2x₀ & b = 2y₀ 
So, x / 2x₀ + y / 2y₀ = 1 
or, x / x₀ + y / y₀ = 2 
Therefore, x * y₀ + y * x₀ = 2 * x₀ * y₀ 
 

下面是上述方法的实现：

C++

// C++ implementation of the approach
#include 
using namespace std;
 
// Function to print the equation
// of the required line
void line(double x0, double y0)
{
    double c = 2 * y0 * x0;
    cout << y0 << "x"
         << " + " << x0 << "y = " << c;
}
 
// Driver code
int main()
{
    double x0 = 4, y0 = 3;
    line(x0, y0);
 
    return 0;
}

Java

// Java implementation of the approach
class GFG
{
     
// Function to print the equation
// of the required line
static void line(double x0, double y0)
{
    double c = (int)(2 * y0 * x0);
    System.out.println(y0 + "x" + " + " +
                       x0 + "y = " + c);
}
 
// Driver code
public static void main(String[] args)
{
    double x0 = 4, y0 = 3;
    line(x0, y0);
}
}
 
// This code is contributed
// by Code_Mech

Python3

# Python 3 implementation of the approach
 
# Function to print the equation
# of the required line
def line(x0, y0):
    c = 2 * y0 * x0
    print(y0, "x", "+", x0, "y=", c)
 
# Driver code
if __name__ == '__main__':
    x0 = 4
    y0 = 3
    line(x0, y0)
     
# This code is contributed by
# Surendra_Gangwar

C#

// C# implementation of the approach
using System;
 
class GFG
{
     
// Function to print the equation
// of the required line
static void line(double x0, double y0)
{
    double c = (int)(2 * y0 * x0);
    Console.WriteLine(y0 + "x" + " + " +
                    x0 + "y = " + c);
}
 
// Driver code
public static void Main(String[] args)
{
    double x0 = 4, y0 = 3;
    line(x0, y0);
}
}
 
/* This code contributed by PrinciRaj1992 */

Javascript

 
// javascript implementation of the approach
 
     
// Function to prvar the equation
// of the required line
function line(x0 , y0)
{
    var c = parseInt(2 * y0 * x0);
    document.write(y0 + "x" + " + " +
                       x0 + "y = " + c);
}
 
// Driver code
var x0 = 4, y0 = 3;
line(x0, y0);
 
 
// This code is contributed by Amit Katiyar
 

输出：

3x + 4y = 24