Final answer:
The center of the circle is (8, 4) and the radius is the square root of 76, or approximately 8.7178.
Step-by-step explanation:
To find the center and radius of the circle given by the equation x² + y² - 16x - 8y + 4 = 0, we should complete the square for both x and y terms. To complete the square for x, we take the coefficient of x, which is -16, divide it by 2 to get -8, and then square it to get 64. Similarly, for y, we take -8, divide by 2 to get -4, and square it to get 16. These squared numbers are then added to both sides of the equation to maintain equality, resulting in:
x² - 16x + 64 + y² - 8y + 16 = 64 + 16 - 4
This simplifies to:
(x - 8)² + (y - 4)² = 76
The equation now represents a circle in the standard form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Thus, the center of our circle is (8, 4) and the radius is the square root of 76, which is √76 or approximately 8.7178.