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.