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The center of the circle with equation \(x^2+y^2=8x-6y-20\) is the point \((x,y)\). What is \(x+y\)?

 Jul 15, 2019
 #1
avatar+105195 
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Rearrange  as

 

x^2 - 8x + y^2 + 6y  = -20       complete the square on x and y

 

x^2 - 8x + 16  + y^2 + 6y + 9  =  -20 + 16  + 9

 

(x - 4)^2  + ( y + 3)^2  =  5

 

The center is  ( 4, -3)  =  ( x , y)

 

So    

 

x + y   =   4 + (-3)   =    1

 

 

cool cool cool

 Jul 15, 2019

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