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

The solution to (x-1)^2+(y-4)^2=4 is Circle with (a,b)=(1,4),r=2

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

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

(a, b) = (1, 4), r = 2

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (1, 4), r = 2

x^{2} + 4 x + y^{2} + 8 y + 16 = 0

(x^{2} + (- 10) x + 25) + (y^{2} + 9 y + \frac{81}{4}) = - 1 + 25 + \frac{81}{4}

x^{2} + 6 x + y^{2} - 2 y - 26 = 0

x^{2} + y^{2} + 9 x - 10 = 0

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

What is (x-1)^2+(y-4)^2=4 ?
The solution to (x-1)^2+(y-4)^2=4 is Circle with (a,b)=(1,4),r=2