The equation of the circle is given by x² + y² = 8x - 6y + 39. To find the center and radius of the circle, we need to rewrite the equation in standard form, which is (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 both x and y terms:
x² - 8x + y² + 6y = 39
(x² - 8x + 16) + (y² + 6y + 9) = 39 + 16 + 9
(x - 4)² + (y + 3)² = 64
Now, compare this with the standard form:
Center: (-4, -3) (since h = 4 and k = -3)
Radius: √64 = 8
Therefore, the correct answer is:
3) Center (-4, -3) and radius 8
