Find Center and Radius of a Circle - 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


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 (-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.

a = b = c =
Decimal Places =
center( , )
radius =
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Updated: 2 April 2013

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