Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.
Simplify as
x^2 - 16x + y^2 + 22y = 86 complete the squre on x, y
x^2 - 16x + 64 + y^2 + 22y + 121 = 86 + 64 + 121
(x - 8)^2 + (y + 11)^2 = 271
This is a circle centered at (8, - 11)
r^2 = 217
Area = pi * r^2 = 271 pi ≈ 851.4
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