Find Tangent at a given point on the curve - GeeksforGeeks

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: 
First find if the given point is on that curve or not.If the point is on that curve then, Find the derivativeCalculate the gradient of the tangent by Putting x, y in dy/dx.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).
First find if the given point is on that curve or not.
If the point is on that curve then, Find the derivative
Calculate the gradient of the tangent by Putting x, y in dy/dx.
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++
Java
Python3
C#
PHP
Javascript
// C++ program for find Tangent// on a curve at given point   #include <bits/stdc++.h>using namespace std;   // function for find Tangentvoid 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 codeint main(){    // declare variable    int A = 2, x = 2, y = 0;       // call function findTangent    findTangent(A, x, y);       return 0;}
// Java program for find Tangent// on a curve at given pointimport java.util.*;import java.lang.*;import java.io.*;   class GFG{    // function for find Tangentstatic 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 codepublic static void main(String args[]){    // declare variable    int A = 2, x = 2, y = 0;        // call function findTangent    findTangent(A, x, y);    } }
# Python3 program for find Tangent# on a curve at given point   # function for find Tangentdef 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# program for find Tangent// on a curve at given point    using System;class GFG{      // function for find Tangentstatic 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 codepublic static void Main(){    // declare variable    int A = 2, x = 2, y = 0;          // call function findTangent    findTangent(A, x, y);      }  }
<?php// PHP program for find Tangent// on a curve at given point   // function for find Tangentfunction 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 findTangentfindTangent($A, $x, $y);   // This code is contributed by Sachin?>
<script> // javascript program for find Tangent// on a curve at given point         // function for find Tangentfunction 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
tufan_gupta2000
ankthon
ukasp
Sach_Code
bunnyram19
Technical Scripter 2018
Geometric
Mathematical
Technical Scripter
Mathematical
Geometric
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Haversine formula to find distance between two points on a sphere
Program to find slope of a line
Equation of circle when three points on the circle are given
Program to find line passing through 2 Points
Maximum Manhattan distance between a distinct pair from N coordinates
Program for Fibonacci numbers
Write a program to print all permutations of a given string
C++ Data Types
Set in C++ Standard Template Library (STL)
Coin Change | DP-7