+16 Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+4x-4y+12
+128578 Simplify as
x^2 -6x + y^2 +10y = 12 + 6 complete the square on x, y
x^2 - 6x + 9 + y^2 + 10y + 25 = 12 + 6+ 9 + 25
(x - 3)^2 + (y + 5)^2 = 52
Ths is a circle with r^2 = 52
Area = pi * r^2 = 52 pi
+16 it seems that you completed the square wrong, you are supposed to get (x-3)^2 and (y-5)^2. After that part, I am stuck though
