Final answer:
For the equation x^2 + y^2 - 2x + 4y - 4 = 0, completing the square yields (x - 1)^2 + (y + 2)^2 = 9. Thus, the circle has a center at (1, -2) and a radius of 3. Similarly, for x^2 + y^2 - 8x + 6 = 0, it becomes (x - 4)^2 + y^2 = 10, indicating a center at (4, 0) and a radius of √10.
Step-by-step explanation:
To identify the center and radius of a circle, we need to write the equation of the circle in the standard form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center and r represents the radius. Let's analyze each given equation: x^2 + y^2 - 2x + 4y - 4 = 0. By completing the square, we can rewrite this equation as (x - 1)^2 + (y + 2)^2 = 9. Therefore, the center is (1, -2) and the radius is 3. 2. x^2 + y^2 - 8x + 6 = 0. Rearranging terms, we have (x - 4)^2 + y^2 = 10. So, the center is (4, 0) and the radius is √10.