Question

Calculate the center of the circle by completing the square of the equation x^2+y^2-10x+4y=20

Answer 1

Start with
x^2 - 10x + y^2 + 4y = 20.

Complete the square for x and y:
(x^2 - 10x + 25) + (y^2 + 4y + 4) = 20 + 25 + 4.

So
(x - 5)^2 + (y + 2)^2 = 49.

Thus the center is (5, -2) (and the radius is 7).