Find Center and Radius of a Circle Given by Equation - Calculator

An online calculator and solver to find the center and radius of a circle given its equation in the form

x^{ 2} + y^{ 2} + a x + b y = c

Complete the Square to Find the Center and Radius

The calculator uses the following idea: completes the squares as follows
x^{ 2} + a x = (x + a/2)^{ 2} - (a/2)^{ 2}
and y^{ 2} + a y = (y + b/2)^{ 2} - (b/2)^{ 2}
Substitute the above into the original equation and write in the standard form of the equation of a circle
(x - h)^{ 2} + (y - k)^{ 2} = r^{ 2}
such that the center has coordinates (h , k) = (-a/2 , -b/2) and radius r such that r^{ 2} = c + (a/2)^{ 2} + (b/2)^{ 2}

How to Use the Calculator?

1 - Enter the coefficients a, b, c and the number of decimal places desired as real number and press "enter". If the given equation is that of a circle, it will give an answer: the x and y coordinates of the center and the radius.