Given two straight lines with co-efficients of their equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 respectively, the task is to check if the straight lines are identical or not.
Examples:
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
Approach:
- Given equations,
a1x + b1y + c1 = 0
a2x + b2y + c2 = 0
- converting them to slope intercept form, we get
y = (-a1/b1)x +(-c1/b1)
y = (-a2/b2)x +(-c2/b2)
- now, if the lines are identical then there slope and intercepts must be equal,
so,
-a1/b1 = -a2/b2
or, a1/a2 = b1/b2
also,
-c1/b1 = -c2/b2
so, c1/c2 = b1/b2
- So, if two given straight lines are identical then there co-efficients should be proportional.
Below is the implementation of the above approach
C++
// C++ program to check if // given two straight lines // are identical or not #include <bits/stdc++.h> 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 |
PHP
<?php // PHP 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 ))
echo "The given straight lines are identical" , "\n" ;
else
echo "The given straight lines are not identical" , "\n" ;
} // Driver Code
$a1 = -2; $b1 = 4;
$c1 = 3; $a2 = -6;
$b2 = 12; $c2 = 9;
idstrt( $a1 , $b1 , $c1 , $a2 , $b2 , $c2 );
// This code is contributed by Ryuga
?> |
Javascript
<script> // 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 </script> |
Output:
The given straight lines are identical
Time Complexity: O(1)
Auxiliary Space: O(1)