Calculate the center of the circle by completing the square of the equation x2+y2−10x+4y=20

Question

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Answer 1

To complete the square of the equation x^2 + y^2 - 10x + 4y = 20, we need to rearrange the terms:

x^2 - 10x + y^2 + 4y = 20
(x^2 - 10x + 25) + (y^2 + 4y + 4) = 20 + 25 + 4
(x - 5)^2 + (y + 2)^2 = 49

Now we have the equation of a circle centered at (5, -2) with a radius of 7. Thus, the center of the circle is at (5, -2).