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Java Program for Finding the vertex, focus and directrix of a parabola
• Last Updated : 05 Dec, 2018

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 . 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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