Calculate the radius of the circle by completing the square of the equation x2+y2−8x+16y=−44
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To complete the square of the equation x^2 + y^2 - 8x + 16y = -44, we first rearrange the equation as follows:
(x^2 - 8x) + (y^2 + 16y) = -44
(x^2 - 8x + 16) + (y^2 + 16y + 64) = -44 + 16 + 64
(x - 4)^2 + (y + 8)^2 = 36
Comparing this to the standard form of the equation of a circle, we can see that the center of the circle is at (4, -8) and the radius is √36 = 6.
Therefore, the radius of the circle is 6.