What is 2x^2+2y^2+36y=-12x-52 ?

The solution to 2x^2+2y^2+36y=-12x-52 is Circle with (a,b)=(-3,-9),r=8

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2x^2+2y^2+36y=-12x-52

2 x^{2} + 2 y^{2} + 36 y = - 12 x - 52

(a, b) = (- 3, - 9), r = 8

Solution steps

2 x^{2} + 2 y^{2} + 36 y = - 12 x - 52

Rewrite

2 x^{2} + 2 y^{2} + 36 y = - 12 x - 52

in the form of the standard circle equation

(x - (- 3))^{2} + (y - (- 9))^{2} = 8^{2}

Therefore the circle properties are:

(a, b) = (- 3, - 9), r = 8

x^{2} + y^{2} + 4 x + 18 y - 171 = 0

16 x^{2} + 16 y^{2} + 96 - 40 y - 315 = 0

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

x^{2} + y^{2} + 6 x + 4 y + 12 = 0

(x + 4)^{2} + (y + 12)^{2} - 16 = 0

What is 2x^2+2y^2+36y=-12x-52 ?
The solution to 2x^2+2y^2+36y=-12x-52 is Circle with (a,b)=(-3,-9),r=8