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.

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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.

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# 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

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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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