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 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++
// 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
// 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
# 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#
// 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 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
Time Complexity : O(1) ,as we are not using any loop.
Auxiliary Space : O(1) ,as we are not using any extra space.
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