求曲线上给定点的切线

给定一条曲线[ y = x(A – x) ]，任务是在该曲线上的给定点 (x, y) 处找到切线，其中 A, x, y 是整数。
例子：

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

方法：

1. 首先找出给定的点是否在该曲线上。
2. 如果该点在该曲线上，则求导数
3. 通过将 x, y 放入 dy/dx 来计算切线的梯度。
4. 通过将切线的梯度和给定点的坐标代入直线方程的梯度点形式，确定切线方程，其中法线方程为 Y – y = ( dy/dx ) * (X – X）。

下面是上述方法的实现：

C++

// C++ program for find Tangent
// on a curve at given point
   
#include 
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

 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

 
// 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.

输出：

y = -2x-4

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