What is the center x^2+y^2-2x+4y+1=0 ?

The center x^2+y^2-2x+4y+1=0 is (1,-2)

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center x^2+y^2-2x+4y+1=0

center

(1, - 2)

Solution steps

x^{2} + y^{2} - 2 x + 4 y + 1 = 0

Rewrite

x^{2} + y^{2} - 2 x + 4 y + 1 = 0

in the form of the standard circle equation

(x - 1)^{2} + (y - (- 2))^{2} = 2^{2}

Therefore the circle properties are:

(a, b) = (1, - 2), r = 2

And the center is:

(1, - 2)