Find the area of the region satisfying the inequality x^2 + y^2 <= 4x + 6y+13 + 10x +2y

Guest May 8, 2022

#1**+2 **

When you move every term to the left-hand side, you get \(x^2 + y^2 - 14x - 8y - 13 \leq 0\).

Complete the squares and you will get \((x - 7)^2 + (y - 4)^2 \leq 78\).

So this is actually just the area enclosed by the circle centered at (7, 4) and with radius \(\sqrt{78}\). Can you take it from here?

MaxWong May 8, 2022