What is the center (x-5)^2+(y-1)^2=49 ?

The center (x-5)^2+(y-1)^2=49 is (5,1)

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center (x-5)^2+(y-1)^2=49

center

(x - 5)^{2} + (y - 1)^{2} = 49

(5, 1)

Solution steps

(x - 5)^{2} + (y - 1)^{2} = 49

Rewrite

(x - 5)^{2} + (y - 1)^{2} = 49

in the form of the standard circle equation

(x - 5)^{2} + (y - 1)^{2} = 7^{2}

Therefore the circle properties are:

(a, b) = (5, 1), r = 7

And the center is:

(5, 1)

x^{2} + (y - 1)^{2} = 36

x^{2} + 4 x + 10 y + y^{2} - 2 = 0

x^{2} + y^{2} + 6 x - 8 y - 2 = 0

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

x^{2} + (y - 1)^{2} = 64