# Python 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 . 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 2Output :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.

__{IDE}__`# Python program to calculate Vertex, Focus and Directrix` ` ` `def` `parabola(a, b, c):` ` ` `print` `(` `"Vertex: ("` `, (` `-` `b ` `/` `(` `2` `*` `a)) , ` `", "` ` ` `,(((` `4` `*` `a ` `*` `c) ` `-` `(b ` `*` `b)) ` `/` `(` `4` `*` `a)) , ` `")"` `)` ` ` ` ` `print` `(` `"Focus: ("` `, (` `-` `b ` `/` `(` `2` `*` `a)) , ` `", "` ` ` `, (((` `4` `*` `a ` `*` `c) ` `-` `(b ` `*` `b) ` `+` `1` `) ` `/` `(` `4` `*` `a)) , ` `")"` `)` ` ` ` ` `print` `(` `"Directrix: y="` ` ` `, (` `int` `)(c ` `-` `((b ` `*` `b) ` `+` `1` `) ` `*` `4` `*` `a )) ` ` ` ` ` `# main()` `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!