Program to Find Vertex, Focus and Directrix of Parabola

Python Program to Find Vertex, Focus and Directrix of Parabola

In the previous article, we have discussed Python Program to Print nth Iteration of Lucas Sequence
Parabola:

A parabola is a curve in a 2D plane that is the same distance from a fixed point called focus as a fixed straight line. The directrix is the name given to this line. A parabola’s general equation is y= ax2+bx+c. In this case, a, b, and c can be any real number.

Given a, b, c  values, the task is to determine Vertex, Focus, and Directrix of the above Given Parabola.

Examples:

Example 1 :

Input :

Given first Term = 5
Given second Term = 2
Given Third Term = 3

Output:

The Vertex of the above Given parabola = ( -0.2 ,  2.8 )
The Focus of the above Given parabola = ( -0.2 ,  2.85 )
The Directrix of the above Given parabola = -97

Example 2 :

Input :

Given first Term = 6
Given second Term = 3
Given Third Term = 1

Output:

The Vertex of the above Given parabola = ( -0.25 ,  0.625 )
The Focus of the above Given parabola = ( -0.25 ,  0.6666666666666666 )
The Directrix of the above Given parabola = -239

Program to Find Vertex, Focus and Directrix of Parabola

Below are the ways to find Vertex, Focus, and Directrix of Parabola.

Method #1: Using Mathematical Formula  (Static Input)

Approach:

  • Give the first number as static input and store it in a variable.
  • Give the second number as static input and store it in another variable.
  • Give the third number as static input and store it in another variable.
  • Print the vertex of the above-given parabola using Standard mathematical formulas.
  • Print the Focus of the above-given parabola using Standard mathematical formulas.
  • Print the Directrix of the above-given parabola using Standard mathematical formulas.
  • The Exit of the Program.

Below is the implementation:

# Give the first number as static input and store it in a variable.
vertx = 5
# Give the second number as static input and store it in another variable.
focs = 2
# Give the third number as static input and store it in another variable.
dirctx = 3
# Print the vertex of the above given parabola using Standard mathematical formulas.
print("The Vertex of the above Given parabola = (", (-focs / (2 * vertx)),
      ", ", (((4 * vertx * dirctx) - (focs * focs)) / (4 * vertx)), ")")
# Print the Focus of the above given parabola using Standard mathematical formulas.
print("The Focus of the above Given parabola = (", (-focs / (2 * vertx)), ", ",
      (((4 * vertx * dirctx) - (focs * focs) + 1) / (4 * vertx)), ")")
# Print the Directrix of the above given parabola using Standard mathematical formulas.
print("The Directrix of the above Given parabola =", (int)
      (dirctx - ((focs * focs) + 1) * 4 * vertx))

Output:

The Vertex of the above Given parabola = ( -0.2 ,  2.8 )
The Focus of the above Given parabola = ( -0.2 ,  2.85 )
The Directrix of the above Given parabola = -97

Method #2: Using Mathematical Formula  (User Input)

Approach:

  • Give the first number as User input using the input() function and store it in a variable.
  • Give the second number as User input using the input() function and store it in another variable.
  • Give the third number as User input using the input() function and store it in another variable.
  • Print the vertex of the above-given parabola using Standard mathematical formulas.
  • Print the Focus of the above-given parabola using Standard mathematical formulas.
  • Print the Directrix of the above-given parabola using Standard mathematical formulas.
  • The Exit of the Program.

Below is the implementation:

# Give the first number as User input using the input() function  and store it in a variable.
vertx = int(input('Enter some Random Number = '))
# Give the second number as User input using the input() function  and store it in another variable.
focs =  int(input('Enter some Random Number = '))
# Give the third number as User input using the input() function  and store it in another variable.
dirctx =  int(input('Enter some Random Number = '))
# Print the vertex of the above given parabola using Standard mathematical formulas.
print("The Vertex of the above Given parabola = (", (-focs / (2 * vertx)),
      ", ", (((4 * vertx * dirctx) - (focs * focs)) / (4 * vertx)), ")")
# Print the Focus of the above given parabola using Standard mathematical formulas.
print("The Focus of the above Given parabola = (", (-focs / (2 * vertx)), ", ",
      (((4 * vertx * dirctx) - (focs * focs) + 1) / (4 * vertx)), ")")
# Print the Directrix of the above given parabola using Standard mathematical formulas.
print("The Directrix of the above Given parabola =", (int)
      (dirctx - ((focs * focs) + 1) * 4 * vertx))

Output:

Enter some Random Number = 6
Enter some Random Number = 3
Enter some Random Number = 1
The Vertex of the above Given parabola = ( -0.25 , 0.625 )
The Focus of the above Given parabola = ( -0.25 , 0.6666666666666666 )
The Directrix of the above Given parabola = -239

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