+0

Circle

0
19
2
+1467

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$.

Jan 12, 2024

#1
+290
+1

$$x^2 + y^2 = 2x - 6y + 6 + 14x - 16y + 80$$

Graph:

We can find the circle radius and we see that it is:

$$\sqrt{271}$$

Area: $$\pi r^2$$

Area = $$271\pi$$, or $$851.371609123$$

Answer: 271π units squared or 851.37 units squared

Jan 12, 2024
#2
+129829
+1

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

Jan 12, 2024
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