What is x^2+y^2-2y-8x-19=0 ?

The solution to x^2+y^2-2y-8x-19=0 is Circle with (a,b)=(4,1),r=6

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x^2+y^2-2y-8x-19=0

x^{2} + y^{2} - 2 y - 8 x - 19 = 0

(a, b) = (4, 1), r = 6

Solution steps

x^{2} + y^{2} - 2 y - 8 x - 19 = 0

Rewrite

x^{2} + y^{2} - 2 y - 8 x - 19 = 0

in the form of the standard circle equation

(x - 4)^{2} + (y - 1)^{2} = 6^{2}

Therefore the circle properties are:

(a, b) = (4, 1), r = 6

x^{2} - 4 x + y^{2} = 3 + 6 y

(x^{2} - 4 x) + (y^{2} - 6 y) = - 9

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

2 x^{2} + 2 y^{2} + 4 x + 12 y - 2 = 0

(x - 12)^{2} + (y - 4)^{2} = 4

What is x^2+y^2-2y-8x-19=0 ?
The solution to x^2+y^2-2y-8x-19=0 is Circle with (a,b)=(4,1),r=6