Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y + 13 - 2x + 8y.
+130071 Rearrange as
x^2 - 4x + 2x + y^2 - 6y - 8y ≤ 13 simplify
x^2 - 2x + y^2 - 14y ≤ 13 complete the square on x and y
x^2 - 2x + 1 + y^2 - 14y + 49 ≤ 13 + 1 + 49
(x - 1)^2 + (y - 7)^2 ≤ 63
This is a circle centered at ( 1, 7) with a radius of sqrt (63)
The inequality tells us that we only want to find the area inside this circle = pi (sqrt (63))^2 = 63 pi units^2
