Java Program for Finding the vertex, focus and directrix of a parabola

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

The standard form of a parabola equation is $y=ax^2+bx+c$ . Given the values of a, b and c; our task is to find the coordinates of vertex, focus and the equation of the directrix.

Example –

Input : 5 3 2
Output : Vertex:(-0.3, 1.55)
         Focus: (-0.3, 1.6)
         Directrix: y=-198
Consult the formula below for explanation.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

// Java program to calculate Vertex, Focus and Directrix 
  
public class TriangularPyramidNumber { 
    public static void parabola(float a, float b, float c) 
    { 
        System.out.println("Vertex: (" + (-b / (2 * a)) + ", "
                           + (((4 * a * c) - (b * b)) / (4 * a)) + ")"); 
  
        System.out.println("Focus: (" + (-b / (2 * a)) + ", "
                           + (((4 * a * c) - (b * b) + 1) / (4 * a)) + ")"); 
  
        System.out.println("Directrix: y="
                           + (int)(c - ((b * b) + 1) * 4 * a)); 
    } 
    public static void main(String[] args) 
    { 
        float a = 5, b = 3, c = 2; 
        parabola(a, b, c); 
    } 
} 
  
// Contributed by _omg 

Output:

Vertex: (-0.3, 1.55)
Focus: (-0.3, 1.6)
Directrix: y=-198

Please refer complete article on Finding the vertex, focus and directrix of a parabola for more details!

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Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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