# C/C++ Program for Finding the vertex, focus and directrix of the parabola?

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A set of points on a plain surface that forms a curve such that any point on that curve is equidistant from a point in the center (called focus) is a parabola.

The general equation for the parabola is

y = ax2 + bx + c

The vertex of a parabola is the coordinate from which it takes the sharpest turn whereas a is the straight-line used to generate the curve.

Focus is the point with is equidistant from all points of the parabola.

Here, we will find the vertex, focus, and directrix of a parabola. There is a mathematical formula that finds all these values. And we will make a program using the mathematical formula for it.

Input:
a = 10,
b = 5,
c = 4
Output:
The vertex: (-0.25, 3.375)
The Focus: (-0.25, 3.4)
y-Directrix:-1036

## Explanation

The mathematical formula for find the vertex, focus and y-direction from the given values of the parabolic figure.

Vertex = {(-b/2a) , (4ac-b2/4a)}

Focus = {(-b/2a), (4ac-b2+1/4a)}

Direction = c - (b2 +1)*4a

## Example

#include <iostream>
using namespace std;
int main() {
float a = 10, b = 5, c = 4;
cout << "The vertex: (" << (-b / (2 * a)) << ", " << (((4 * a * c) - (b * b)) / (4 * a)) << ")\n";
cout << "The Focus: (" << (-b / (2 * a)) << ", " << (((4 * a * c) - (b * b) + 1) / (4 * a)) << ")\n";
cout << "y-Directrix:" << c - ((b * b) + 1) * 4 * a;
}