Dado el radio y las coordenadas del Centro de un círculo. Encuentre el cuadrante en el que se encuentra otra coordenada dada (X, Y) con respecto al centro del círculo si el punto se encuentra dentro del círculo. De lo contrario, imprime un error «Se encuentra fuera del círculo».
Si el punto se encuentra en el centro del círculo, emite 0 o si el punto se encuentra en cualquiera de los ejes y dentro del círculo, emite el siguiente cuadrante en dirección antihoraria.
Ejemplos:
Entrada: Centro = (0, 0), Radio = 10
(X, Y) = (10, 10)
Salida: Se encuentra fuera del círculo
Entrada: Centro = (0, 3), Radio = 2
(X, Y) = (1, 4)
Salida: 1 (cuadrante I)
Enfoque:
Sea el centro (x’, y’)
La ecuación del círculo es 
– (Ec. 1)
De acuerdo con esta ecuación,
Si 
el punto (x, y) se encuentra fuera del círculo
Si 
el punto (x, y) se encuentra en el círculo
Si 
el punto (x, y) se encuentra dentro del círculo
Para comprobar la posición del punto con respecto al círculo:-
1. Put given coordinates in equation 1. 2. If it is greater than 0 coordinate lies outside circle. 3. If point lies inside circle find the quadrant within the circle. Check the point with respect to centre of circle.
A continuación se muestra la implementación de la idea anterior:
C++
// CPP Program to find the quadrant of
// a given coordinate with respect to the
// centre of a circle
#include <bits/stdc++.h>
using namespace std;
// Thus function returns the quadrant number
int getQuadrant(int X, int Y, int R, int PX, int PY)
{
// Coincides with center
if (PX == X && PY == Y)
return 0;
int val = pow((PX - X), 2) + pow((PY - Y), 2);
// Outside circle
if (val > pow(R, 2))
return -1;
// 1st quadrant
if (PX > X && PY >= Y)
return 1;
// 2nd quadrant
if (PX <= X && PY > Y)
return 2;
// 3rd quadrant
if (PX < X && PY <= Y)
return 3;
// 4th quadrant
if (PX >= X && PY < Y)
return 4;
}
// Driver Code
int main()
{
// Coordinates of centre
int X = 0, Y = 3;
// Radius of circle
int R = 2;
// Coordinates of the given point
int PX = 1, PY = 4;
int ans = getQuadrant(X, Y, R, PX, PY);
if (ans == -1)
cout << "Lies Outside the circle" << endl;
else if (ans == 0)
cout << "Coincides with centre" << endl;
else
cout << ans << " Quadrant" << endl;
return 0;
}
Java
// Java Program to find the quadrant of
// a given coordinate with respect to the
// centre of a circle
import java.io.*;
class GFG {
// Thus function returns
// the quadrant number
static int getQuadrant(int X, int Y,
int R, int PX,
int PY)
{
// Coincides with center
if (PX == X && PY == Y)
return 0;
int val = (int)Math.pow((PX - X), 2) +
(int)Math.pow((PY - Y), 2);
// Outside circle
if (val > Math.pow(R, 2))
return -1;
// 1st quadrant
if (PX > X && PY >= Y)
return 1;
// 2nd quadrant
if (PX <= X && PY > Y)
return 2;
// 3rd quadrant
if (PX < X && PY <= Y)
return 3;
// 4th quadrant
if (PX >= X && PY < Y)
return 4;
return 0;
}
// Driver Code
public static void main (String[] args)
{
// Coordinates of centre
int X = 0, Y = 3;
// Radius of circle
int R = 2;
// Coordinates of the given point
int PX = 1, PY = 4;
int ans = getQuadrant(X, Y, R, PX, PY);
if (ans == -1)
System.out.println( "Lies Outside the circle");
else if (ans == 0)
System.out.println( "Coincides with centre");
else
System.out.println( ans +" Quadrant");
}
}
// This code is contributed by anuj_67.
Python3
# Python3 Program to find the
# quadrant of a given coordinate
# w.rt. the centre of a circle
import math
# Thus function returns the
# quadrant number
def getQuadrant(X, Y, R, PX, PY):
# Coincides with center
if (PX == X and PY == Y):
return 0;
val = (math.pow((PX - X), 2) +
math.pow((PY - Y), 2));
# Outside circle
if (val > pow(R, 2)):
return -1;
# 1st quadrant
if (PX > X and PY >= Y):
return 1;
# 2nd quadrant
if (PX <= X and PY > Y):
return 2;
# 3rd quadrant
if (PX < X and PY <= Y):
return 3;
# 4th quadrant
if (PX >= X and PY < Y):
return 4;
# Driver Code
# Coordinates of centre
X = 0;
Y = 3;
# Radius of circle
R = 2;
# Coordinates of the given po
PX = 1;
PY = 4;
ans = getQuadrant(X, Y, R, PX, PY);
if (ans == -1) : print("Lies Outside the circle");
elif (ans == 0) : print("Coincides with centre");
else:print(ans, "Quadrant");
# This code is contributed by mits
C#
// C# Program to find the quadrant of
// a given coordinate with respect to
// the centre of a circle
using System;
class GFG {
// Thus function returns
// the quadrant number
static int getQuadrant(int X, int Y,
int R, int PX, int PY)
{
// Coincides with center
if (PX == X && PY == Y)
return 0;
int val = (int)Math.Pow((PX - X), 2)
+ (int)Math.Pow((PY - Y), 2);
// Outside circle
if (val > Math.Pow(R, 2))
return -1;
// 1st quadrant
if (PX > X && PY >= Y)
return 1;
// 2nd quadrant
if (PX <= X && PY > Y)
return 2;
// 3rd quadrant
if (PX < X && PY <= Y)
return 3;
// 4th quadrant
if (PX >= X && PY < Y)
return 4;
return 0;
}
// Driver Code
public static void Main ()
{
// Coordinates of centre
int X = 0, Y = 3;
// Radius of circle
int R = 2;
// Coordinates of the given point
int PX = 1, PY = 4;
int ans =
getQuadrant(X, Y, R, PX, PY);
if (ans == -1)
Console.WriteLine( "Lies Outside"
+ " the circle");
else if (ans == 0)
Console.WriteLine( "Coincides "
+ "with centre");
else
Console.WriteLine( ans +
" Quadrant");
}
}
// This code is contributed by anuj_67.
PHP
<?php
// PHP Program to find the quadrant of
// a given coordinate with respect to the
// centre of a circle
// Thus function returns the
// quadrant number
function getQuadrant($X, $Y, $R,
$PX, $PY)
{
// Coincides with center
if ($PX == $X and $PY == $Y)
return 0;
$val = pow(($PX - $X), 2) +
pow(($PY - $Y), 2);
// Outside circle
if ($val > pow($R, 2))
return -1;
// 1st quadrant
if ($PX > $X and $PY >= $Y)
return 1;
// 2nd quadrant
if ($PX <= $X and $PY > $Y)
return 2;
// 3rd quadrant
if ($PX < $X and $PY <= $Y)
return 3;
// 4th quadrant
if ($PX >= $X and $PY < $Y)
return 4;
}
// Driver Code
// Coordinates of centre
$X = 0; $Y = 3;
// Radius of circle
$R = 2;
// Coordinates of the given po$
$PX = 1;
$PY = 4;
$ans = getQuadrant($X, $Y, $R,
$PX, $PY);
if ($ans == -1)
echo "Lies Outside the circle" ;
else if ($ans == 0)
echo "Coincides with centre" ;
else
echo $ans , " Quadrant" ;
// This code is contributed by anuj_67.
?>
Javascript
<script>
// Javascript Program to find the quadrant of
// a given coordinate with respect to the
// centre of a circle
// Thus function returns the quadrant number
function getQuadrant( X, Y, R, PX, PY)
{
// Coincides with center
if (PX == X && PY == Y)
return 0;
let val = Math.pow((PX - X), 2) + Math.pow((PY - Y), 2);
// Outside circle
if (val > Math.pow(R, 2))
return -1;
// 1st quadrant
if (PX > X && PY >= Y)
return 1;
// 2nd quadrant
if (PX <= X && PY > Y)
return 2;
// 3rd quadrant
if (PX < X && PY <= Y)
return 3;
// 4th quadrant
if (PX >= X && PY < Y)
return 4;
}
// Driver Code
// Coordinates of centre
let X = 0, Y = 3;
// Radius of circle
let R = 2;
// Coordinates of the given point
let PX = 1, PY = 4;
let ans = getQuadrant(X, Y, R, PX, PY);
if (ans == -1)
document.write("Lies Outside the circle" + "</br>");
else if (ans == 0)
document.write("Coincides with centre" + "</br>");
else
document.write(ans + " Quadrant" + "</br>");
</script>
Producción:
1 Quadrant
Publicación traducida automáticamente
Artículo escrito por coolsaiification y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA