程序来找到抛物线的Latus直肠的长度

给定a，b和c的系数X ² ， X和抛物线方程中的常数项$y = a\times x^{2} + b\times x + c$ ，任务是找到抛物线的Latus直肠的长度。

例子：

Input: a = 3, b = 5, c = 1
Output: 0.333333

Input: a = 4, b = 0, c = 4
Output: 0.25

方法：可以根据以下观察结果解决给定问题：

Observation:

• The Latus rectum of a parabola is the perpendicular line to the axis and at the focus of parabola and its length is equal to 4 times the distance between the focus and vertex of the parabola.

• Therefore, the task is reduced to find the distance between focus and vertex of the parabola using formula:
  • $d = sqrt( (x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} )$

请按照以下步骤解决问题：

• 初始化两个变量，例如顶点和焦点，以存储抛物线的顶点和焦点的坐标。
• 找到顶点的坐标和抛物线的焦点，并将其存储在相应的变量中。
• 初始化一个变量，例如length ，并将其设置为抛物线的顶点和焦点之间的距离的4倍。
• 打印长度值作为答案。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
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 vertex
        = { (-b / (2 * a)),
            (((4 * a * c) - (b * b)) / (4 * a)) };
 
    // Stores the co-ordinates of
    // the focus of parabola
    pair 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

输出：

0.333333

时间复杂度： O(1)
辅助空间： O(1)