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