Find equation of the circle passing through the points

Question

Find an equation of the circle passing through the points (2, 3), (−1, 6), and (5, 2).

Answer 1

(x-h)^2+ (y-k)^2 = r^2 is the general equation of a circle with center = (h,k) and radius = 4

(2-h)^2 + (3-k)^2 = r^2 for the point (2,3)

(-1-h)^2 + (6-k)^2 = r^2 for the point (-1,6)

(5-h)^2 + (2-k)^2 = r^2 for the point (5,2)

3 equations 3 unknowns

solve by substitution, elimination, or matrix algebra

following is from substitution and elimination

h=-3.75, k=-2.75, r^2 = 1586/16, r= about 9.96 = radius

circle center = (-3.75,-2.75)

(x-3.75)^2 + (y-2.75)^2 = 1586/16

is the circle's equation going through the 3 given points

it may help to plot the points, and see if the answer is reasonable.

actually it looks very reasonable, center in the right quadrant IV and roughly same distance to each of the three points

possible mistake(s) somewhere though

the substitution, elimination method sometimes gets tedious with easily made errors

no guarantees the above is correct