Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.
x2+y2=2x−6y+6+14x−16y+80
Graph:
We can find the circle radius and we see that it is:
√271
Area: πr2
Area = 271π, 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
+1729 
