HomeData Modelling & AIPython Program for Finding the vertex, focus and directrix of a parabola

Data Modelling & AI Data Structure & Algorithm

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

25 June 2025

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.

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