Find the area of the region enclosed by the graph of \(x^2 + y^2 = 2x - 6y + 6\).
+128474 x^2 + y^2 = 2x - 6y + 6 rearrange as
x^2 - 2x + y^2 + 6y = 6 completete the square on x and y
x^2 -2x + 1 + y^2 + 6y + 9 = 6 + 1 + 9
(x -1)^2 + ( y + 3)^2 = 16
This is a circle centered at (1, -3) with a radius of 4
The area is
pi r^2 = pi * 4^2 = 16 pi units ^2
