Circle defined by 3 points calculator




Equation of a circle passing through 3 points (x_{1}, y_{1}) (x_{2}, y_{2}) and (x_{3}, y_{3}) summary


The coefficients A, B, C and D can be found by solving the following determinants: 

Center point (x, y) and the radius of a circle passing through 3 points (x_{1}, y_{1}) (x_{2}, y_{2}) and (x_{3}, y_{3}) are: 
Example 1  Circle Defined by 3 Points


Find the equation of a circle that passes through the points (⎯3 , 4) , (4 , 5) and (1 , ⎯4).



Example 2  Circle Defined by 3 Points
Find the equation of a circle and its center and radius if the circle passes through the points (3 , 2) ,
(6 , 3) and (0 , 3). 

After dividing all terms by 6 we get: A = 1 B =−6 C = −14 D = 33.
And the equation of the circle is: x^{2} + y^{2} ⎯ 6x ⎯ 14y + 33 = 0 In order to find the radius of the circle use the general circle equation and perform some basic algebraic steps and with the help of the square form (a + b)^{2} = a^{2} + 2ab + b^{2} we get
The last equation is a circle with the center and radius equals to (notice the minus sign at x and y):
The equation of the circle can be presented by the center and the radius as: (x ⎯ 3)^{2} + (y ⎯ 7)^{2} = 5^{2}
