+617 Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+4x-4y+12
+37063 Re-arrange as
x^2 -6x + y^2 +10y = 18 Complete the square for x and y
(x-3)^2 + (y+5)^2 = 18 +9 +25
(x-3)^2 + (y+5)^2 = 52 <==== this is a circle centered at 3,-5 with radius = sqrt (52)
Area of a circle = pi r^2
= pi (sqrt (52) )^2 = 52 pi = 163.4 units^2
