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C++ program to find the vertex, focus and directrix of a parabola
In this article, we will be discussing a program to find the vertex, focus and directrix of a parabola when the coefficients of its equation is given.
Parabola is a curve whose all points on the curve are equidistant from a single point called focus.
As we know the general equation for a parabola is
y = ax2 + bx + c
For this equation, the following are defined as :
Vertex -(-b/2a, 4ac - b2/4a) Focus - (-b/2a, 4ac - b2+1/4a) Directrix - y = c - (b2 +1)4a
Example
#include <iostream>
using namespace std;
void calc_para(float a, float b, float c) {
cout << "Vertex- (" << (-b / (2 * a)) << ", " << (((4 * a* c) - (b * b)) / (4 * a)) << ")" << endl;
cout << "Focus- (" << (-b / (2 * a)) << ", " << (((4 * a* c) - (b * b) + 1) / (4 * a)) << ")" << endl;
cout << "Directrix- y=" << c - ((b * b) + 1) * 4 * a <<endl;
}
int main() {
float a = 23, b = 34, c = 5;
calc_para(a, b, c);
return 0;
}Output
Vertex- (-0.73913, -7.56522) Focus- (-0.73913, -7.55435) Directrix- y=-106439
Updated on: 03-Oct-2019
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