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Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+6+4x-4y+12

 Apr 23, 2024
 #1
avatar+128772 
+1

Simplify as

 

x^2 -6x + y^2 +10y  =  12 + 6               complete the square on x, y

 

x^2 - 6x + 9 + y^2 + 10y + 25 =  12  + 6+ 9 + 25

 

(x - 3)^2  + (y + 5)^2  =  52

 

Ths  is a  circle with  r^2  = 52

 

Area =   pi * r^2   =  52 pi

 

cool cool

 Apr 23, 2024
edited by CPhill  Apr 23, 2024
edited by CPhill  Apr 23, 2024
 #2
avatar+20 
0

it seems that you completed the square wrong, you are supposed to get (x-3)^2 and (y-5)^2. After that part, I am stuck though

gaberiellz  Apr 23, 2024
 #3
avatar+128772 
+1

Sorry....see corrections

 

 

cool cool cool

CPhill  Apr 23, 2024

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