Given a curve [ y = x(A – x) ], the task is to find normal at a given point ( x, y) on that curve, where A is an integer number and x, y also any integer.
Examples:
Input: A = 2, x = 2, y = 0
Output: 2y = x - 2
Since y = x(2 - x)
y = 2x - x^2 differentiate it with respect to x
dy/dx = 2 - 2x put x = 2, y = 0 in this equation
dy/dx = 2 - 2* 2 = -2
equation => (Y - 0 ) = ((-1/-2))*( Y - 2)
=> 2y = x -2
Input: A = 3, x = 4, y = 5
Output: Not possible
Point is not on that curve
Approach: First we need to find given point is on that curve or not if the point is on that curve then:
- We need to differentiate that equation that point don’t think too much for differentiation of this equation if you analyze then you find that dy/dx always become A – 2x.
- Put x, y in dy/dx.
- Equation of normal is Y – y = -(1/( dy/dx )) * (X – x).
Below is the implementation of the above approach:
C++
// C++ program for find curve// at given point#include <bits/stdc++.h>using namespace std;// function for find normalvoid findNormal(int A, int x, int y){ // differentiate given equation int dif = A - x * 2; // check that point on the curve or not if (y == (2 * x - x * x)) { // if differentiate is negative if (dif < 0) cout << 0 - dif << "y = " << "x" << (0 - x) + (y * dif); else if (dif > 0) // differentiate is positive cout << dif << "y = " << "-x+" << x + dif * y; // differentiate is zero else cout << "x = " << x; } // other wise normal not found else cout << "Not possible";}// Driver codeint main(){ // declare variable int A = 2, x = 2, y = 0; // call function findNormal findNormal(A, x, y); return 0;} |
Java
// Java program for find curve// at given pointimport java.io.*;class GFG {// function for find normalstatic void findNormal(int A, int x, int y){ // differentiate given equation int dif = A - x * 2; // check that point on the curve or not if (y == (2 * x - x * x)) { // if differentiate is negative if (dif < 0) System.out.print( (0 - dif) + "y = " + "x" +((0 - x) + (y * dif))); else if (dif > 0) // differentiate is positive System.out.print( dif + "y = " + "-x+" + (x + dif * y)); // differentiate is zero else System.out.print( "x = " +x); } // other wise normal not found else System.out.println( "Not possible");} // Driver code public static void main (String[] args) { // declare variable int A = 2, x = 2, y = 0; // call function findNormal findNormal(A, x, y);; }}// This Code is contributed by inder_verma.. |
Python3
# Python 3 program for find curve# at given point# function for find normaldef findNormal(A, x, y): # differentiate given equation dif = A - x * 2 # check that point on the curve or not if (y == (2 * x - x * x)): # if differentiate is negative if (dif < 0): print(0 - dif, "y =", "x", (0 - x) + (y * dif)) elif (dif > 0): # differentiate is positive print(dif, "y =", "- x +", x + dif * y) # differentiate is zero else: print("x =", x) # other wise normal not found else: print("Not possible")# Driver codeif __name__ == '__main__': # declare variable A = 2 x = 2 y = 0 # call function findNormal findNormal(A, x, y) # This code is contributed By# Surendra_Gangwar |
C#
// C# program for find curve // at given point using System;class GFG{ // function for find normalstatic void findNormal(int A, int x, int y){ // differentiate given equation int dif = A - x * 2; // check that point on // the curve or not if (y == (2 * x - x * x)) { // if differentiate is negative if (dif < 0) Console.Write((0 - dif) + "y = " + "x" + ((0 - x) + (y * dif))); else if (dif > 0) // differentiate is positive Console.Write(dif + "y = " + "-x + " + (x + dif * y)); // differentiate is zero else Console.Write("x = " + x); } // other wise normal not found else Console.WriteLine("Not possible");}// Driver codestatic public void Main (){ // declare variable int A = 2, x = 2, y = 0; // call function findNormal findNormal(A, x, y);}}// This code is contributed by ajit |
PHP
<?php// PHP program for find curve // at given point // function for find normal function findNormal($A, $x, $y) { // differentiate given equation $dif = $A - $x * 2; // check that point on the // curve or not if ($y == (2 * $x - $x * $x)) { // if differentiate is negative if ($dif < 0) echo (0 - $dif), "y = ", "x" , (0 - $x) + ($y * $dif); else if ($dif > 0) // differentiate is positive echo $dif , "y = ", "-x+" ,( $x + $dif * $y); // differentiate is zero else echo "x = " , $x; } // other wise normal not found else echo "Not possible"; } // Driver code // declare variable $A = 2;$x = 2;$y = 0; // call function findNormal findNormal($A, $x, $y); // This code is contributed by ajit?> |
Javascript
<script> // Javascript program for find curve at given point // function for find normal function findNormal(A, x, y) { // differentiate given equation let dif = A - x * 2; // check that point on // the curve or not if (y == (2 * x - x * x)) { // if differentiate is negative if (dif < 0) document.write((0 - dif) + "y = " + "x" + ((0 - x) + (y * dif))); else if (dif > 0) // differentiate is positive document.write(dif + "y = " + "-x + " + (x + dif * y)); // differentiate is zero else document.write("x = " + x); } // other wise normal not found else document.write("Not possible"); } // declare variable let A = 2, x = 2, y = 0; // call function findNormal findNormal(A, x, y); </script> |
Output:
2y = x-2
Time Complexity : O(1) ,as we are not using any loop.
Auxiliary Space : O(1) ,as we are not using any extra space.
Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!
… [Trackback]
[…] Here you will find 76796 additional Info to that Topic: geeksforgeeks.org/find-normal-at-a-given-point-on-the-curve/ […]
… [Trackback]
[…] Read More Info here to that Topic: geeksforgeeks.org/find-normal-at-a-given-point-on-the-curve/ […]
… [Trackback]
[…] Read More here on that Topic: geeksforgeeks.org/find-normal-at-a-given-point-on-the-curve/ […]
… [Trackback]
[…] Here you will find 93015 more Info to that Topic: geeksforgeeks.org/find-normal-at-a-given-point-on-the-curve/ […]