# Equation of circle from centre and radius

Given the centre of circle (x1, y1) and its radius r, find the equation of the circle having centre (x1, y1) and having radius r.

**Examples:**

Input :x1 = 2, y1 = -3, r = 8

Output :x^2 + y^2 – 4*x + 6*y = 51.

Input :x1 = 0, y1 = 0, r = 2

Output :x^2 + y^2 – 0*x + 0*y = 4.

**Approach:**

Given the centre of circle (x1, y1) and its radius r, we have to find the equation of the circle having centre (x1, y1) and having radius r.

the equation of circle having centre (x1, y1) and having radius r is given by :-

on expanding above equation

on arranging above we get

Below is the implemetation of above approach:

## C++

`// CPP program to find the equation ` `// of circle. ` `#include <iostream> ` `using` `namespace` `std; ` ` ` `// Function to find the equation of circle ` `void` `circle_equation(` `double` `x1, ` `double` `y1, ` `double` `r) ` `{ ` ` ` `double` `a = -2 * x1; ` ` ` ` ` `double` `b = -2 * y1; ` ` ` ` ` `double` `c = (r * r) - (x1 * x1) - (y1 * y1); ` ` ` ` ` `// Printing result ` ` ` `cout << ` `"x^2 + ("` `<< a << ` `" x) + "` `; ` ` ` `cout << ` `"y^2 + ("` `<< b << ` `" y) = "` `; ` ` ` `cout << c << ` `"."` `<< endl; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `double` `x1 = 2, y1 = -3, r = 8; ` ` ` `circle_equation(x1, y1, r); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to find the equation ` `// of circle. ` `import` `java.util.*; ` ` ` `class` `solution ` `{ ` ` ` ` ` `// Function to find the equation of circle ` `static` `void` `circle_equation(` `double` `x1, ` `double` `y1, ` `double` `r) ` `{ ` ` ` `double` `a = -` `2` `* x1; ` ` ` ` ` `double` `b = -` `2` `* y1; ` ` ` ` ` `double` `c = (r * r) - (x1 * x1) - (y1 * y1); ` ` ` ` ` `// Printing result ` ` ` `System.out.print(` `"x^2 + ("` `+a+ ` `" x) + "` `); ` ` ` `System.out.print(` `"y^2 + ("` `+b + ` `" y) = "` `); ` ` ` `System.out.println(c +` `"."` `); ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String arr[]) ` `{ ` ` ` `double` `x1 = ` `2` `, y1 = -` `3` `, r = ` `8` `; ` ` ` `circle_equation(x1, y1, r); ` ` ` `} ` ` ` `} ` |

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## Python3

# Python3 program to find the

# equation of circle.

# Function to find the

# equation of circle

def circle_equation(x1, y1, r):

a = -2 * x1;

b = -2 * y1;

c = (r * r) – (x1 * x1) – (y1 * y1);

# Printing result

print(“x^2 + (“, a, “x) + “, end = “”);

print(“y^2 + (“, b, “y) = “, end = “”);

print(c, “.”);

# Driver code

x1 = 2;

y1 = -3;

r = 8;

circle_equation(x1, y1, r);

# This code is contributed

# by mits

## C#

`// C# program to find the equation ` `// of circle. ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the equation of circle ` `public` `static` `void` `circle_equation(` `double` `x1, ` ` ` `double` `y1, ` ` ` `double` `r) ` `{ ` ` ` `double` `a = -2 * x1; ` ` ` ` ` `double` `b = -2 * y1; ` ` ` ` ` `double` `c = (r * r) - (x1 * x1) - (y1 * y1); ` ` ` ` ` `// Printing result ` ` ` `Console.Write(` `"x^2 + ("` `+ a + ` `" x) + "` `); ` ` ` `Console.Write(` `"y^2 + ("` `+ b + ` `" y) = "` `); ` ` ` `Console.WriteLine(c + ` `"."` `); ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main(` `string` `[]arr) ` `{ ` ` ` `double` `x1 = 2, y1 = -3, r = 8; ` ` ` `circle_equation(x1, y1, r); ` `} ` `} ` ` ` `// This code is contributed ` `// by SoumkMondal ` |

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## PHP

`<?php ` `// PHP program to find the equation ` `// of circle. ` ` ` `// Function to find the ` `// equation of circle ` `function` `circle_equation(` `$x1` `, ` `$y1` `, ` `$r` `) ` `{ ` ` ` `$a` `= -2 * ` `$x1` `; ` ` ` ` ` `$b` `= -2 * ` `$y1` `; ` ` ` ` ` `$c` `= (` `$r` `* ` `$r` `) - (` `$x1` `* ` `$x1` `) - ` ` ` `(` `$y1` `* ` `$y1` `); ` ` ` ` ` `// Printing result ` ` ` `echo` `"x^2 + ("` `. ` `$a` `. ` `" x) + "` `; ` ` ` `echo` `"y^2 + ("` `. ` `$b` `. ` `" y) = "` `; ` ` ` `echo` `$c` `. ` `"."` `. ` `"\n"` `; ` `} ` ` ` `// Driver code ` `$x1` `= 2; ` `$y1` `= -3; ` `$r` `= 8; ` `circle_equation(` `$x1` `, ` `$y1` `, ` `$r` `); ` ` ` `// This code is contributed ` `// by Akanksha Rai ` `?> ` |

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**Output:**

x^2 + (-4 x) + y^2 + (6 y) = 51.

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