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 identicalvoid 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 Codeint 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 notclass GFG{// Function to check if they are identicalstatic 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 Codepublic 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 identicaldef 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 Codea1, b1 = -2, 4c1, a2 = 3,-6b2, c2 = 12,9idstrt(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 notusing 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 identicalfunction 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)
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