# Find normal at a given point on the curve in C++

Suppose we have a curve like y = x(A - x), we have to find the normal at a given point (x,y) on that curve. Here A is an integer number, x and y are also integers.

To solve this, we have the check that the given point is on the curve or not, if so, then find the differentiation of that curve, so it will be −

$$\frac{\text{d}y}{\text{d}x}=A-2x$$

Then put x and y into the dy/dx, then find the normal using this equation −

$$Y-y=-\lgroup\frac{\text{d}x}{\text{d}y}\rgroup*\lgroup X-x \rgroup$$

## Example

Live Demo

#include<iostream>
using namespace std;
void getNormal(int A, int x, int y) {
int differentiation = A - x * 2;
if (y == (2 * x - x * x)) {
if (differentiation < 0)
cout << 0 - differentiation << "y = " << "x" << (0 - x) + (y * differentiation);
else if (differentiation > 0)
cout << differentiation << "y = " << "-x+" << x + differentiation * y;
else
cout << "x = " << x;
}
else
cout << "Not possible";
}
int main() {
int A = 5, x = 2, y = 0;
cout << "Equation of normal is: ";
getNormal(A, x, y);
}

## Output

Equation of normal is: 1y = -x+2