Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.
\(x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80\)
Graph:
We can find the circle radius and we see that it is:
\(\sqrt{271}\)
Area: \(\pi r^2\)
Area = \(271\pi\), or \(851.371609123\)
Answer: 271π units squared or 851.37 units squared
Simplify as
x^2 - 16x + y^2 + 22y = 80 complete the square on x, y
x^2 -16x + 64 + y^2 + 22y + 121 = 80 + 64 + 121
(x - 8)^2 + (y + 11)^2 = 265
The center is (8, -11) and the area is 265 pi ≈ 832.5
+1537 
