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

 Aug 10, 2024
 #1
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First, let's simplify the equation a bit. We get

\(x^2 - 16x + y^2 + 22y = 86\)

 

Completing the square for BOTH x and y, we get the equation

\(x^2 - 16x + 64 + y^2 + 22y + 121 = 86 + 64 + 121 \\ (x - 8)^2 + (y + 11)^2 = 271\)

 

This is a  circle centered at (8, - 11) with r^2  = 217

 

Now, we can find the area. We simply have

\(Area = pi * r^2 = 271 pi ≈ 851.4\)

 

Thanks! :)

 Aug 10, 2024
edited by NotThatSmart  Aug 10, 2024

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