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Finding the vertex, focus and directrix of a parabola in C++
In this tutorial, we are going to learn how to find the vertex, focus, and directrix of a parabola. We are given constants of the parabola equation x, y, and z.
There are straightforward formulas to find the vertex, focus, and directrix. Let's them.
Vertex − (-y/2x, 4xz-y^2/4x)
Focus − (-y/2x, 4xz-y^2+1/4x)
Directrix − z-(y^2+1)4x
Example
Let's see the code.
#include <iostream>
using namespace std;
void findParabolaProperties(float x, float y, float z) {
cout << "Vertex: (" << -y/(2*x) << ", " << (((4*x*z) - (y*y))/4*x) << ")" << endl;
cout << "Focus: (" << -y/(2*x) << ", " << (((4*x*z) - (y*y)+1)/4*x) << ")" << endl;
cout << "Directrix: " << z-((y*y)+1)*4*x << endl;
}
int main() {
float x = 6, y = 4, z = 7;
findParabolaProperties(x, y, z);
return 0;
}Output
If you run the above code, then you will get the following result.
Vertex: (-0.333333, 228) Focus: (-0.333333, 229.5) Directrix: -401
Conclusion
If you have any queries in the tutorial, mention them in the comment section
Updated on: 29-Dec-2020
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