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Find Tangent at a given point on the curve

  • Last Updated : 24 May, 2021

Given a curve [ y = x(A – x) ], the task is to find tangent at given point (x, y) on that curve, where A, x, y are integers.
Examples: 
 

Input: A = 2, x = 2, y = 0
Output: y = -2x - 4
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 ) = ((-2))*( Y - 2)
                => y = -2x -4

Input: A = 3, x = 4, y = 5
Output: Not possible
    Point is not on that curve

 

 

Approach:
 



  1. First find if the given point is on that curve or not.
  2. If the point is on that curve then, Find the derivative
  3. Calculate the gradient of the tangent by Putting x, y in dy/dx.
  4. Determine the equation of the tangent by substituting the gradient of the tangent and the coordinates of the given point into the gradient-point form of the straight line equation, where Equation of normal is Y – y = ( dy/dx ) * (X – x).

Below is the implementation of the above approach:

C++




// C++ program for find Tangent
// on a curve at given point
   
#include <bits/stdc++.h>
using namespace std;
   
// function for find Tangent
void findTangent(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 << "y = "
                 << dif << "x" << (x * dif) + (y);
   
        else if (dif > 0)
   
            // differentiate is positive
            cout << "y = "
                 << dif << "x+" << -x * dif + y;
   
        // differentiate is zero
        else
            cout << "Not possible";
    }
}
   
// Driver code
int main()
{
    // declare variable
    int A = 2, x = 2, y = 0;
   
    // call function findTangent
    findTangent(A, x, y);
   
    return 0;
}

Java




// Java program for find Tangent
// on a curve at given point
import java.util.*;
import java.lang.*;
import java.io.*;
   
class GFG
{
    
// function for find Tangent
static void findTangent(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.println( "y = "
                 + dif + "x" + (x * dif + y));
    
        else if (dif > 0)
    
            // differentiate is positive
            System.out.println( "y = "
                 + dif + "x+" + -x * dif + y);
    
        // differentiate is zero
        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 findTangent
    findTangent(A, x, y);
    
}

Python3




# Python3 program for find Tangent
# on a curve at given point
   
# function for find Tangent
def findTangent(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("y =",dif,"x",(x * dif) + (y))
   
        # differentiate is positive
        elif dif > 0 :
   
            print("y =",dif,"x+",-x * dif + y)
   
        # differentiate is zero
        else :
               
            print("Not Possible")
               
   # Driver code    
if __name__ == "__main__" :
   
    # declare variable
    A, x, y = 2, 2, 0
   
    # call function findTangent
    findTangent(A, x, y)
                    
# This code is contributed by
# ANKITRAI1

C#




// C# program for find Tangent
// on a curve at given point
    
using System;
class GFG
{
      
// function for find Tangent
static void findTangent(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( "y = "
                 + dif + "x" + (x * dif + y)+"\n");
      
        else if (dif > 0)
      
            // differentiate is positive
            Console.Write( "y = "
                 + dif + "x+" + -x * dif + y+"\n");
      
        // differentiate is zero
        else
            Console.Write("Not possible"+"\n");
    }
}
      
// Driver code
public static void Main()
{
    // declare variable
    int A = 2, x = 2, y = 0;
      
    // call function findTangent
    findTangent(A, x, y);
      
}  
}

PHP




<?php
// PHP program for find Tangent
// on a curve at given point
   
// function for find Tangent
function findTangent($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 "y = ", $dif , "x" ,
                  ($x * $dif) + ($y);
   
        else if ($dif > 0)
   
            // differentiate is positive
            echo "y = ",
                $dif , "x+" , -$x * $dif + $y;
   
        // differentiate is zero
        else
            echo "Not possible";
    }
}
   
// Driver code
   
// declare variable
$A = 2;
$x = 2;
$y = 0;
   
// call function findTangent
findTangent($A, $x, $y);
   
// This code is contributed by Sachin
?>

Javascript




<script>
 
// javascript program for find Tangent
// on a curve at given point
    
     
// function for find Tangent
function findTangent( A,  x,  y)
{
    // differentiate given equation
    var 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( "y = "
                 + dif + "x" + (x * dif + y)+"\n");
      
        else if (dif > 0)
      
            // differentiate is positive
            document.write( "y = "
                 + dif + "x+" + -x * dif + y+"\n");
      
        // differentiate is zero
        else
            document.write("Not possible"+"\n");
    }
}
      
// Driver code
 
    // declare variable
    var A = 2, x = 2, y = 0;
      
    // call function findTangent
    findTangent(A, x, y);
 
// This code is contributed by bunnyram19.
</script>

Output:

y = -2x-4

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