Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y + 6 + 4x - 8y.
Rearrange as
x^2 - 6x + y^2 + 14y = 6 complete the square on x, y
(x^2 - 6x + 9) + ( y^2 + 14y + 49 ) = 6 + 9 + 49
(x -3)^2 + ( y + 7)^2 = 64
This is a circle centered at ( 3 , -7) with a radius of 8
The area enclosed = pi * 8^2 = 64 pi units^2
