What is 2x^2+2y^2+12x-2y=0 ?

The solution to 2x^2+2y^2+12x-2y=0 is Circle with (a,b)=(-3, 1/2),r=(sqrt(37))/2

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2x^2+2y^2+12x-2y=0

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

(a, b) = (- 3, \frac{1}{2}), r = \frac{37}{2}

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - (- 3))^{2} + (y - \frac{1}{2})^{2} = (\frac{37}{2})^{2}

Therefore the circle properties are:

(a, b) = (- 3, \frac{1}{2}), r = \frac{37}{2}

x^{2} + y^{2} + 2 x - 10 y + 21 = 0

4 x^{2} + 4 y^{2} + 8 x - 8 y + 7 = 0

x^{2} + y^{2} + 8 x - 4 y + 19 = 0

(x - 3)^{2} + (y + 4)^{2} = 4

2 x^{2} + 2 y^{2} + 10 x - 2 y = 7

What is 2x^2+2y^2+12x-2y=0 ?
The solution to 2x^2+2y^2+12x-2y=0 is Circle with (a,b)=(-3, 1/2),r=(sqrt(37))/2