What is the center (x-1)^2+(y-4)^2=25 ?

The center (x-1)^2+(y-4)^2=25 is (1,4)

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center (x-1)^2+(y-4)^2=25

center

(x - 1)^{2} + (y - 4)^{2} = 25

(1, 4)

Solution steps

(x - 1)^{2} + (y - 4)^{2} = 25

Rewrite

(x - 1)^{2} + (y - 4)^{2} = 25

in the form of the standard circle equation

(x - 1)^{2} + (y - 4)^{2} = 5^{2}

Therefore the circle properties are:

(a, b) = (1, 4), r = 5

And the center is:

(1, 4)

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

(x + 3)^{2} + (y - 4)^{2} = 7

x^{2} + y^{2} - 10 x + 6 y - 2 = 0

x^{2} + y^{2} = 3 x + 4 y

(x - 4)^{2} + (y - 5)^{2} = 36