Final answer:
To find the center and radius of the circle, rewrite the equation in standard form (x-h)² + (y-k)² = r². Completing the square for x and y terms, the center is (2,4) and the radius is √15.
Step-by-step explanation:
To find the center and radius of the circle, we need to rewrite the equation in the standard form: (x-h)² + (y-k)² = r², where (h,k) represents the center of the circle and r represents the radius.
For the given equation:
x² - 4x + y² - 8y + 11 = 0
Completing the square for x terms, we get:
(x² - 4x + 4) + y² - 8y + 11 = 4 + 11
(x - 2)² + (y - 4)² = 15
Therefore, the center of the circle is (2,4) and the radius is √15.