# Finding the vertex, focus and directrix of a parabola in Python Program

PythonServer Side ProgrammingProgramming

## Problem statement

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

The vertex of a parabola is the coordinate from which it takes the sharpest turn whereas y=a is the straight-line used to generate the curve.

A directrix a fixed line used in describing a curve or surface.

Now let’s see the implementation −

## Example

Live Demo

def findparabola(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 = 7
b = 5
c = 3

findparabola(a, b, c)

## Output

Vertex: ( -0.35714285714285715 , 2.107142857142857 )
Focus: ( -0.35714285714285715 , 2.142857142857143 )
Directrix: y= -725

All the variables & the function are declared in the global scope as shown in the figure below.