# Find normal at a given point on the curve

Given a curve [ y = x(A – x) ], the task is to find normal at given point ( x, y) on that curve, here A is any integer number and x, y also any integer.

Examples:

```Input: A = 2, x = 2, y = 0
Output: 2y = x - 2
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 ) = ((-1/-2))*( Y - 2)
=> 2y = x -2

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: First we need to find given point is on that curve or not if the point is on that curve then:

1. We need to differentiate that equation that point don’t think too much for differentiation of this equation if you analyze then you find that dy/dx always become A – 2x.
2. Put x, y in dy/dx.
3. Equation of normal is Y – y = -(1/( dy/dx )) * (X – x).

Below is the implementation of the above approach:

## C++

 `// C++ program for find curve ` `// at given point ` `#include ` `using` `namespace` `std; ` ` `  `// function for find normal ` `void` `findNormal(``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 << 0 - dif << ``"y = "` `                 ``<< ``"x"` `<< (0 - x) + (y * dif); ` ` `  `        ``else` `if` `(dif > 0) ` ` `  `            ``// differentiate is positive ` `            ``cout << dif << ``"y = "` `                 ``<< ``"-x+"` `<< x + dif * y; ` ` `  `        ``// differentiate  is zero ` `        ``else` `            ``cout << ``"x = "` `<< x; ` `    ``} ` ` `  `    ``// other wise normal not found ` `    ``else` `        ``cout << ``"Not possible"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``// declare variable ` `    ``int` `A = 2, x = 2, y = 0; ` ` `  `    ``// call function findNormal ` `    ``findNormal(A, x, y); ` `    ``return` `0; ` `} `

## Java

 `// Java program for find curve ` `// at given point ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `// function for find normal ` `static` `void` `findNormal(``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.print( (``0` `- dif) + ``"y = "` `                ``+ ``"x"` `+((``0` `- x) + (y * dif))); ` ` `  `        ``else` `if` `(dif > ``0``) ` ` `  `            ``// differentiate is positive ` `            ``System.out.print( dif + ``"y = "` `                ``+ ``"-x+"` `+ (x + dif * y)); ` ` `  `        ``// differentiate is zero ` `        ``else` `            ``System.out.print( ``"x = "` `+x); ` `    ``} ` ` `  `    ``// other wise normal not found ` `    ``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 findNormal ` `    ``findNormal(A, x, y);; ` `    ``} ` `} ` `// This Code is contributed by inder_verma.. `

## Python3

 `# Python 3 program for find curve ` `# at given point ` ` `  `# function for find normal ` `def` `findNormal(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``(``0` `-` `dif, ``"y ="``, ``"x"``,  ` `                 ``(``0` `-` `x) ``+` `(y ``*` `dif)) ` ` `  `        ``elif` `(dif > ``0``): ` `             `  `            ``# differentiate is positive ` `            ``print``(dif, ``"y ="``, ``"- x +"``,  ` `                        ``x ``+` `dif ``*` `y) ` ` `  `        ``# differentiate is zero ` `        ``else``: ` `            ``print``(``"x ="``, x) ` ` `  `    ``# other wise normal not found ` `    ``else``: ` `        ``print``(``"Not possible"``) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `     `  `    ``# declare variable ` `    ``A ``=` `2` `    ``x ``=` `2` `    ``y ``=` `0` ` `  `    ``# call function findNormal ` `    ``findNormal(A, x, y) ` `     `  `# This code is contributed By ` `# Surendra_Gangwar `

## C#

 `// C# program for find curve  ` `// at given point  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// function for find normal ` `static` `void` `findNormal(``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((0 - dif) + ``"y = "` `+  ` `                   ``"x"` `+ ((0 - x) + (y * dif))); ` ` `  `        ``else` `if` `(dif > 0) ` ` `  `            ``// differentiate is positive ` `            ``Console.Write(dif + ``"y = "` `+  ` `                          ``"-x + "` `+ (x + dif * y)); ` ` `  `        ``// differentiate is zero ` `        ``else` `            ``Console.Write(``"x = "` `+ x); ` `    ``} ` ` `  `    ``// other wise normal not found ` `    ``else` `        ``Console.WriteLine(``"Not possible"``); ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `    ``// declare variable ` `    ``int` `A = 2, x = 2, y = 0; ` `     `  `    ``// call function findNormal ` `    ``findNormal(A, x, y); ` `} ` `} ` ` `  `// This code is contributed by ajit `

## PHP

 ` 0)  ` ` `  `            ``// differentiate is positive  ` `            ``echo` `\$dif` `, ``"y = "``, ` `                 ``"-x+"` `,( ``\$x` `+ ``\$dif` `* ``\$y``);  ` ` `  `        ``// differentiate is zero  ` `        ``else` `            ``echo` `"x = "` `, ``\$x``;  ` `    ``}  ` ` `  `    ``// other wise normal not found  ` `    ``else` `        ``echo` `"Not possible"``;  ` `}  ` ` `  `// Driver code  ` ` `  `// declare variable  ` `\$A` `= 2; ` `\$x` `= 2; ` `\$y` `= 0;  ` ` `  `// call function findNormal  ` `findNormal(``\$A``, ``\$x``, ``\$y``);  ` ` `  `// This code is contributed by ajit ` `?> `

Output:

```2y = x-2
```

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