Final answer:
The equation of the circle that passes through the points (3,-2), (1, -2), and (0,0) is found by solving a system of equations derived from the general circle equation, resulting in the equation (x - 2)² + (y + 2)² = 2.
Step-by-step explanation:
To find the equation of the circle that passes through the points (3,-2), (1, -2), and (0,0), we need to solve a system of equations to find the values of a, b, and c in the general equation of a circle, which is a(x² + y²) + bx + cy + d = 0. By plugging in the points into the equation:
- For (3, -2): 9a + 3b - 2c + d = 0
- For (1, -2): a + b - 2c + d = 0
- For (0, 0): d = 0
Since we already know that d is 0 from the third equation, we can substitute into the first two and solve the system of linear equations.
After solving the equations, we end up with a circle equation (x - 2)² + (y + 2)² = 2, which represents the circle passing through the given points.