Python program to find vertex, focus and directrix of parabola

In this tutorial, we will learn how to find vertex, focus and directrix of parabola in Python.

What is a parabola?

A parabola is a curve in a 2D plane such that every point on that plane is at the same distance from a fixed point called focus as from a fixed straight line. This line is called the directrix. A general equation of a parabola is y= px2+qx+r. Here p, q, and r can be any real number.

In this tutorial, we will be given values of p, q, and r for the equation and we will have to find the vertex, focus and the equation of directrix. Let’s see how we can do this.

Python program to calculate the vertex, focus, and directrix of a parabola

We can calculate the vertex and the focus of a parabola using formulae for them. We can also find the equation of the directrix as shown in the code. The below program calculates the vertex, focus and the directrix of a parabola with given coefficients p, q, and r. See the code.

def parabola(p, q, r):
    print("Vertex of the parabola is (", (-q/(2*p)) , "," , (((4*p*r)-(q*q))/(4*p)) , ")" )
    
    print("Focus of the parabola is (", (-q/(2*p)) , "," , (((4*p*r)-(q*q)+1)/(4*p)) , ")" ) 
    
    print("Equation of the directrix is y = ", (int)(r-((q*q)+1)*4*p)) 
    
p = 2
q = 4
r = 6

parabola(p, q, r)

The output of the above example program is given below.

Vertex of the parabola is ( -1.0 , 4.0 )
Focus of the parabola is ( -1.0 , 4.125 )
Equation of the directrix is y =  -130

You can change the values of p, q, and r for different outputs.

Note that the above code only works for the parabola of the form y= px2+qx+r. For the parabola of the form x= py2+qy+r, we need to use different formulae.

Thank you.

Also, read: How to plot ROC Curve using Sklearn library in Python

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