Problema Solution
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 provided by our tutors
Let the center and radius of the circle be O(x,y)
|AO| = |BO| = |CO|
|AO|^2 = |BO|^2 = |CO|^2
(x - 0)^2 + (y - 0)^2 = (x -(-3))^2 + (y - 0)^2 = (x - 1)^2 + (y - 2)^2
x^2 + y^2 = x^2 + 6x + 9 + y^2 = x^2 - 2x + 1 + y^2 - 4y + 4
6x + 9 = 0
5 - 2x - 4y = 0
........
........
x = -1.5
y = 2
The center of the circle is O(-1.5, 2).