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Find the area of the region enclosed by the graph of \(x^2 + y^2 = 2x - 6y + 6\).

 Apr 10, 2020

Best Answer 

 #2
avatar+111329 
+2

x^2 + y^2   = 2x - 6y + 6       rearrange as

 

x^2 - 2x   +  y^2  +  6y  =   6      completete the square on  x and  y

 

x^2 -2x + 1   +  y^2  + 6y + 9  =  6 + 1 + 9

 

(x -1)^2  +  ( y + 3)^2   =  16

 

This is a circle  centered at   (1, -3)   with a radius  of  4

 

The  area  is

 

pi r^2  =     pi * 4^2 =    16 pi units ^2

 

 

cool cool cool

 Apr 10, 2020
 #1
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0

The region is a circle with radius sqrt(12), so the area is 12*pi.

 Apr 10, 2020
 #2
avatar+111329 
+2
Best Answer

x^2 + y^2   = 2x - 6y + 6       rearrange as

 

x^2 - 2x   +  y^2  +  6y  =   6      completete the square on  x and  y

 

x^2 -2x + 1   +  y^2  + 6y + 9  =  6 + 1 + 9

 

(x -1)^2  +  ( y + 3)^2   =  16

 

This is a circle  centered at   (1, -3)   with a radius  of  4

 

The  area  is

 

pi r^2  =     pi * 4^2 =    16 pi units ^2

 

 

cool cool cool

CPhill Apr 10, 2020

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