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 = ax<sup>2</sup> + 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

解释

根据给定的抛物线图形的数值，找到顶点、焦点和y方向的数学公式。

顶点 = {(-b/2a) , (4ac-b²/4a)}

焦点 = {(-b/2a), (4ac-b²+1/4a)}

方向 = c - (b² +1)*4a

示例

#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;
}