What is the center (x-1)^2+(y+4)^2=9 ?

The center (x-1)^2+(y+4)^2=9 is (1,-4)

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center (x-1)^2+(y+4)^2=9

center

(x - 1)^{2} + (y + 4)^{2} = 9

(1, - 4)

Solution steps

(x - 1)^{2} + (y + 4)^{2} = 9

Rewrite

(x - 1)^{2} + (y + 4)^{2} = 9

in the form of the standard circle equation

(x - 1)^{2} + (y - (- 4))^{2} = 3^{2}

Therefore the circle properties are:

(a, b) = (1, - 4), r = 3

And the center is:

(1, - 4)

x^{2} + y^{2} - x - 6 y + 9 = 0

(x + 4)^{2} + (y + 3)^{2} = 17

(x - 1)^{2} + (y + 4)^{2} = 16

4 x^{2} + 16 x + 15 + 4 y^{2} + 6 y = 0

(x + 4)^{2} + (y + 3)^{2} = 25