检查给定的两条直线是否相同

给定两条分别具有系数a1x + b1y + c1 = 0和a2x + b2y + c2 = 0的直线，任务是检查这些直线是否相同。
例子：

Input: a1 = -2, b1 = 4, c1 = 3, a2 = -6, b2 = 12, c2 = 9 
Output: The given straight lines are identical
Input: a1 = 12, b1 = 3, c1 = 8, a2 = 7, b2 = -12, c2 = 0 
Output: The given straight lines are not identical

方法：

1. 给定方程式
   a1x + b1y + c1 = 0
   a2x + b2y + c2 = 0
2. 将它们转换为斜率截距形式，我们得到
   y =(-a1 / b1)x +(-c1 / b1)
   y =(-a2 / b2)x +(-c2 / b2)
3. 现在，如果线是相同的，那么斜率和截距必须相等，
   所以，
   -a1 / b1 = -a2 / b2
   或者，a1 / a2 = b1 / b2
   还，
   -c1 / b1 = -c2 / b2
   因此，c1 / c2 = b1 / b2
4. 因此，如果两条给定的直线相同，则系数应该成比例。
   $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

下面是上述方法的实现

C++

// C++ program to check if
// given two straight lines
// are identical or not
 
#include 
using namespace std;
 
// Function to check if they are identical
void idstrt(double a1, double b1,
            double c1, double a2,
            double b2, double c2)
{
    if ((a1 / a2 == b1 / b2)
        && (a1 / a2 == c1 / c2)
        && (b1 / b2 == c1 / c2))
        cout << "The given straight"
             << " lines are identical"
             << endl;
 
    else
        cout << "The given straight"
             << " lines are not identical"
             << endl;
}
 
// Driver Code
int main()
{
    double a1 = -2, b1 = 4,
           c1 = 3, a2 = -6,
           b2 = 12, c2 = 9;
    idstrt(a1, b1, c1, a2, b2, c2);
    return 0;
}

Java

// Java program to check if
// given two straight lines
// are identical or not
class GFG
{
 
// Function to check if they are identical
static void idstrt(double a1, double b1,
                    double c1, double a2,
                    double b2, double c2)
{
    if ((a1 / a2 == b1 / b2)
        && (a1 / a2 == c1 / c2)
        && (b1 / b2 == c1 / c2))
        System.out.println( "The given straight"
        +" lines are identical");
 
    else
        System.out.println("The given straight"
            + " lines are not identical");
}
 
// Driver Code
public static void main(String[] args)
{
    double a1 = -2, b1 = 4,
            c1 = 3, a2 = -6,
            b2 = 12, c2 = 9;
    idstrt(a1, b1, c1, a2, b2, c2);
}
}
 
// This code has been contributed by 29AjayKumar

Python3

# Python3 program to check if
# given two straight lines
# are identical or not
 
# Function to check if they are identical
def idstrt(a1, b1, c1, a2, b2, c2):
    if ((a1 // a2 == b1 // b2) and
        (a1 // a2 == c1 // c2) and
        (b1 // b2 == c1 // c2)):
        print("The given straight lines",
                         "are identical");
    else:
        print("The given straight lines",
                     "are not identical");
 
# Driver Code
a1, b1 = -2, 4
c1, a2 = 3,-6
b2, c2 = 12,9
idstrt(a1, b1, c1, a2, b2, c2)
 
# This code is contributed
# by mohit kumar

C#

// C# program to check if
// given two straight lines
// are identical or not
using System;
 
class GFG
{
 
// Function to check if they are identical
static void idstrt(double a1, double b1,
                    double c1, double a2,
                    double b2, double c2)
{
    if ((a1 / a2 == b1 / b2)
        && (a1 / a2 == c1 / c2)
        && (b1 / b2 == c1 / c2))
        Console.WriteLine( "The given straight"
        +" lines are identical");
 
    else
        Console.WriteLine("The given straight"
            + " lines are not identical");
}
 
// Driver Code
public static void Main(String[] args)
{
    double a1 = -2, b1 = 4,
            c1 = 3, a2 = -6,
            b2 = 12, c2 = 9;
    idstrt(a1, b1, c1, a2, b2, c2);
}
}
 
// This code contributed by Rajput-Ji

Javascript

 
// javascript program to check if
// given two straight lines
// are identical or not
 
 
// Function to check if they are identical
function idstrt(a1 , b1,
                    c1 , a2,
                    b2 , c2)
{
    if ((a1 / a2 == b1 / b2)
        && (a1 / a2 == c1 / c2)
        && (b1 / b2 == c1 / c2))
        document.write( "The given straight"
        +" lines are identical");
 
    else
        document.write("The given straight"
            + " lines are not identical");
}
 
// Driver Code
  
 
var a1 = -2, b1 = 4,
        c1 = 3, a2 = -6,
        b2 = 12, c2 = 9;
idstrt(a1, b1, c1, a2, b2, c2);
 
// This code contributed by Princi Singh
 

输出：

The given straight lines are identical