What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?
Simplify as
x^2 + 12x + y^2 + 2y = 10 complete the square on x, y
x^2 + 12x + 36 + y^2 + 2y + 1 = 10 + 36 + 1
(x + 6)^2 + (y + 1)^2 = 47
47 = r^2
Area of this circle = pi r^2 = pi * 47 = 47 pi
+2653 
