Complete the square in the equation for both x and y to locate the center. Then, find the midpoint of AB to see if they are one and the same. The center of the circle would be the midpoint of the diameter.
Center is at (1, 2)
Midpoint of AB =
Substitute (4, 4) into your original equation to see if it makes a true statement
Angle ACB is an inscribed angle in a semicircle, therefore 90 degrees.
See Earboth's post.