Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y + 6 + 8x - 2y - 5x + 8y + 208.
Simplify as
x^2 - 5x + y^2 = 214 complete the square on x
x^2 - 5x + 25/4 + y^2 = 214 + 25/4
(x - 5/2)^2 + y^2 = 881/4
The area = (881/4) pi ≈ 691/94
+475 
