Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y+13 + 2x - 2y.
+128408 4x + 6y + 13 + 2x -2y simplifies to
6x + 4y + 13
So
x^2 + y^2 ≤ 6x + 4y + 13
x^2 -6x + y^2 -4y ≤ 13 complete the square on x and y
x^2 - 6x + 9 + y^2 - 4y + 4 ≤ 13 + 9 + 4
(x - 3)^2 + (y - 2)^2 ≤ 26
This is just the area inside the circle with a center of ( 3, 2) and a radius of sqrt (26)
See here : https://www.desmos.com/calculator/0c8kf8nfll
The area is pi (sqrt (26))^2 = 26 pi
