The center of the circle with equation x2+y2=8x−6y−20 is the point (x,y) . What is x+y ?
x2+y2=8x−6y−20x2−8x+y2+6y=−20x2−8x+16+y2+6y+9=−20+16+9(x−4)(x−4)+(y+3)(y+3)=5(x−4)2+(y+3)2=5
So the center is located at (4,-3)
4 + (-3) = 4 - 3 = 1
Bingo!
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