The equation of the circle given is x² + y² + 2x - 16y + 49 = 0.
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) is the center of the circle and r is the radius.
First, complete the square for the x and y terms in the equation:
x² + 2x + y² - 16y = -49
(x² + 2x + 1) + (y² - 16y + 64) = -49 + 1 + 64
(x + 1)² + (y - 8)² = 16
(x + 1)² + (y - 8)² = 4²
Now, we can see that the center of the circle is (-1, 8) and the radius is 4.
Therefore, the correct answer is:
2) center (-1, 8) and radius 4
