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
r^2 = 10 + 36 + 1 = 47
Area = r^2 * pi = 47 pi ≈ 147.65
+1286 
