+1084 Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.
+1946 First, let's simplify the equation a bit. We get
x2−16x+y2+22y=86
Completing the square for BOTH x and y, we get the equation
x2−16x+64+y2+22y+121=86+64+121(x−8)2+(y+11)2=271
This is a circle centered at (8, - 11) with r^2 = 217
Now, we can find the area. We simply have
Area=pi∗r2=271pi≈851.4
Thanks! :)
