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 $y=ax^2+bx+c$ . 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.

# 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!

My Personal Notes

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

Recommended Posts: