Programa para hallar la longitud del Latus Rectum de una Parábola

Dados a, b y c los coeficientes de X ² , X y el término constante en la ecuación general de la parábola $y = a\times x^{2} + b\times x + c$ , la tarea es encontrar la longitud del Latus Rectum de la parábola .

Ejemplos:

Entrada: a =3, b = 5, c = 1
Salida: 0,333333

Entrada: a = 4, b = 0, c = 4
Salida: 0,25

Enfoque: El problema dado se puede resolver con base en las siguientes observaciones:

Observación:

El Latus rectum de una parábola es la línea perpendicular al eje y al foco de la parábola y su longitud es igual a 4 veces la distancia entre el foco y el vértice de la parábola.

Por lo tanto, la tarea se reduce a encontrar la distancia entre el foco y el vértice de la parábola usando la fórmula:

$d = sqrt( (x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} )$

Siga los pasos a continuación para resolver el problema:

Inicialice dos variables, digamos vértice y foco para almacenar las coordenadas del vértice y el foco de la parábola.
Encuentra las coordenadas del vértice y el foco de la parábola y guárdalas en las variables correspondientes.
Inicialice una variable, digamos length , y configúrela en 4 veces la distancia entre el vértice y el foco de la parábola.
Imprime el valor de longitud como respuesta.

A continuación se muestra la implementación del enfoque anterior:

C++

// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate distance
// between two points
float distance(float x1, float y1,
               float x2, float y2)
{
    // Calculating distance
    return sqrt((x2 - x1) * (x2 - x1)
                + (y2 - y1) * (y2 - y1));
}
 
// Function to calculate length of
// the latus rectum of a parabola
float lengthOfLatusRectum(float a,
                          float b, float c)
{
    // Stores the co-ordinates of
    // the vertex of the parabola
    pair<float, float> vertex
        = { (-b / (2 * a)),
            (((4 * a * c) - (b * b)) / (4 * a)) };
 
    // Stores the co-ordinates of
    // the focus of parabola
    pair<float, float> focus
        = { (-b / (2 * a)),
            (((4 * a * c) - (b * b) + 1) / (4 * a)) };
 
    // Print the distance between focus and vertex
    cout << 4 * distance(
                    focus.first, focus.second,
                    vertex.first, vertex.second);
}
 
// Driver Code
int main()
{
    // Given a, b & c
    float a = 3, b = 5, c = 1;
 
    // Function call
    lengthOfLatusRectum(a, b, c);
 
    return 0;
}

Java

// Java program for the above approach
class GFG{
  static class pair
  {
    float first;
    float second;
    public pair(float first, float second) 
    {
      this.first = first;
      this.second = second;
    }   
  }
 
  // Function to calculate distance
  // between two points
  static float distance(float x1, float y1,
                        float x2, float y2)
  {
 
    // Calculating distance
    return (float) Math.sqrt((x2 - x1) * (x2 - x1)
                             + (y2 - y1) * (y2 - y1));
  }
 
  // Function to calculate length of
  // the latus rectum of a parabola
  static void lengthOfLatusRectum(float a,
                                  float b, float c)
  {
 
    // Stores the co-ordinates of
    // the vertex of the parabola
    pair vertex
      = new pair( (-b / (2 * a)),
                 (((4 * a * c) - (b * b)) / (4 * a)) );
 
    // Stores the co-ordinates of
    // the focus of parabola
    pair focus
      = new pair( (-b / (2 * a)),
                 (((4 * a * c) - (b * b) + 1) / (4 * a)) );
 
    // Print the distance between focus and vertex
    System.out.print(4 * distance(
      (float)focus.first, (float)focus.second,
      (float)vertex.first, (float)vertex.second));
  }
 
  // Driver Code
  public static void main(String[] args)
  {
 
    // Given a, b & c
    float a = 3, b = 5, c = 1;
 
    // Function call
    lengthOfLatusRectum(a, b, c);
 
  }
}
 
// This code is contributed by 29AjayKumar

Python3

# Python 3 program for the above approach
from math import sqrt
 
# Function to calculate distance
# between two points
def distance(x1, y1, x2, y2):
   
    # Calculating distance
    return sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1))
 
# Function to calculate length of
# the latus rectum of a parabola
def lengthOfLatusRectum(a, b, c):
   
    # Stores the co-ordinates of
    # the vertex of the parabola
    vertex =  [(-b / (2 * a)), (((4 * a * c) - (b * b)) / (4 * a))]
 
    # Stores the co-ordinates of
    # the focus of parabola
    focus = [(-b / (2 * a)), (((4 * a * c) - (b * b) + 1) / (4 * a))]
 
    # Print the distance between focus and vertex
    print("{:.6f}".format(4 * distance(focus[0], focus[1], vertex[0], vertex[1])))
 
# Driver Code
if __name__  == "__main__":
   
    # Given a, b & c
    a = 3
    b = 5
    c = 1
 
    # Function call
    lengthOfLatusRectum(a, b, c)
     
    # This code is contributed by bgangwar59.

C#

// C# program for the above approach
using System;
 
public class GFG{
  class pair
  {
    public float first;
    public float second;
    public pair(float first, float second) 
    {
      this.first = first;
      this.second = second;
    }   
  }
 
  // Function to calculate distance
  // between two points
  static float distance(float x1, float y1,
                        float x2, float y2)
  {
 
    // Calculating distance
    return (float) Math.Sqrt((x2 - x1) * (x2 - x1)
                             + (y2 - y1) * (y2 - y1));
  }
 
  // Function to calculate length of
  // the latus rectum of a parabola
  static void lengthOfLatusRectum(float a,
                                  float b, float c)
  {
 
    // Stores the co-ordinates of
    // the vertex of the parabola
    pair vertex
      = new pair( (-b / (2 * a)),
                 (((4 * a * c) - (b * b)) / (4 * a)) );
 
    // Stores the co-ordinates of
    // the focus of parabola
    pair focus
      = new pair( (-b / (2 * a)),
                 (((4 * a * c) - (b * b) + 1) / (4 * a)) );
 
    // Print the distance between focus and vertex
    Console.Write(4 * distance(
      (float)focus.first, (float)focus.second,
      (float)vertex.first, (float)vertex.second));
  }
 
  // Driver Code
  public static void Main(String[] args)
  {
 
    // Given a, b & c
    float a = 3, b = 5, c = 1;
 
    // Function call
    lengthOfLatusRectum(a, b, c);
 
  }
}
 
  
 
// This code is contributed by 29AjayKumar

Javascript

<script>
    // Javascript program for the above approach
     
    // Function to calculate distance
    // between two points
    function distance(x1, y1, x2, y2)
    {
        // Calculating distance
        return Math.sqrt((x2 - x1) * (x2 - x1)
                    + (y2 - y1) * (y2 - y1));
    }
 
    // Function to calculate length of
    // the latus rectum of a parabola
    function lengthOfLatusRectum(a, b, c)
    {
        // Stores the co-ordinates of
        // the vertex of the parabola
        let vertex
            = [ (-b / (2 * a)),
                (((4 * a * c) - (b * b)) / (4 * a)) ];
 
        // Stores the co-ordinates of
        // the focus of parabola
        let focus
            = [ (-b / (2 * a)),
                (((4 * a * c) - (b * b) + 1) / (4 * a)) ];
 
        // Print the distance between focus and vertex
        document.write((4 * distance(
                        focus[0], focus[1],
                        vertex[0], vertex[1])).toFixed(6));
    }
     
    // Given a, b & c
    let a = 3, b = 5, c = 1;
  
    // Function call
    lengthOfLatusRectum(a, b, c);
  
 // This code is contributed by divyeshrabadiya07.
</script>

Producción:

0.333333

Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)

Publicación traducida automáticamente

Artículo escrito por sam_2200 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

C++

Java

Python3

C#

Javascript

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