在曲线的给定点处找到切线

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

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. 首先找到给定点是否在该曲线上。
2. 如果该点在该曲线上，则找到导数
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来确定切线方程，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);
      
   }  
   }

   Python 3

   # 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 
   ?>

   输出：

   y = -2x-4