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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 $x+y$?

 Jan 15, 2018
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\($x^2+y^2=8x-6y-20$\)

 

Write 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

 Jan 15, 2018

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