Find the area of the region enclosed by the graph of x^2 + y^2 = 2x - 6y + 6 + 4x - 8y.
+9519 \(x^2 + y^2 = 2x - 6y + 6 +4x - 8y\\ x^2 + y^2 = 6x - 14y + 6\\ x^2 - 6x + y^2 + 14y - 6 = 0\\ (x^2 -6x + 9) + (y^2 +14y + 49) = 64\\ (x - 3)^2 + (y + 7)^2 = 8^2 \)
The graph is a circle centred at (3, -7) and with radius 8 units.
The required area is \(\pi \cdot 8^2 = \boxed{64\pi\text{ sq. units}}\)
