What is y^2+2x+x^2=24y-120 ?

The solution to y^2+2x+x^2=24y-120 is Circle with (a,b)=(-1,12),r=5

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y^2+2x+x^2=24y-120

y^{2} + 2 x + x^{2} = 24 y - 120

(a, b) = (- 1, 12), r = 5

Solution steps

y^{2} + 2 x + x^{2} = 24 y - 120

Rewrite

y^{2} + 2 x + x^{2} = 24 y - 120

in the form of the standard circle equation

(x - (- 1))^{2} + (y - 12)^{2} = 5^{2}

Therefore the circle properties are:

(a, b) = (- 1, 12), r = 5

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

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

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

(x - 8)^{2} + (y + 3)^{2} = 121

x^{2} + y^{2} - 4 x - 8 y - 5 = 0

What is y^2+2x+x^2=24y-120 ?
The solution to y^2+2x+x^2=24y-120 is Circle with (a,b)=(-1,12),r=5