Question

Circle O, with center (x, y), passes through the points A(0, 0), B(–3, 0), and C(1, 2). Find the coordinates of the center of the circle. In your final answer, include all formulas and calculations used to find Point O, x, y), the center of circle O.

Answer 1

(x + 3/2)² + (y - 2)² = 25/4

hope this helps :D

Answer 2

(x + 3/2)² + (y - 2)² = 25/4

Explanation:

(x - h)² + (y - k)² = r²

(0,0)

(0 - h)² + (0 - k)² = r²

h² + k² = r²

(-3,0)

(-3 - h)² + (0 - k)² = r²

9 + 6h + h² + k² = r²

9 + 6h + r² = r²

9 + 6h = 0

h = -9/6 = -3/2

(1,2)

(1 - h)² + (2 - k)² = r²

1 - 2h + h² + 4 - 4k + k² = r²

5 - 2h - 4k + h² + k² = h² + k²

5 - 2(-3/2) - 4k = 0

8 = 4k

k = 2

(x - (-3/2))² + (y - 3)² = r²

(x + 3/2)² + (y - 2)² = r²

Use any point to find r²

(0 + 3/2)² + (0 - 2)² = r²

9/4 + 4 = r²

r² = 25/4

(x + 3/2)² + (y - 2)² = 25/4