the main formula of the circle's equation is (x-a)²+ (y-b)² = R² where C(a, b) is the center of the circle R is the radius
if a point A(x', y') passes through the circle, so the equation of the circle can be written as (x'-a)²+ (y'-b)² = R², and that is a main formula.
<span>Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2), so we have exactly three equation: </span> (0-x)² + (0-y)² = R², circle O passes through A x²+y²= R² (-3 -x)² + (0-y)² = R², circle O passes through B (-3 -x)² + (y)² = R² (1-x)² + (2-y)² = R², circle O passes through A (1-x)² + (2-y)² = R²
and we know that R= OA = OC= OB, OA=R= sqrt( (0-x)² + (0-y)² ) = OB = sqrt((-3 -x)² + (0-y)²), this implies
x²+y² = (-3 -x)² + (0-y)² , it implies x² = 9+ x² + 6x , and then -9/6=x, x= -3/2 and when OA = OC x²+y² =(1-x)² + (2-y)² so, x²+y² =1+x²-2x +4+y²-4y, therefore -5= -2x -4y -5= -2x -4y, when x = -3 /2 we obtain y = 2
