What is 2x^2+2y^2+12y-2y-3=0 ?

The solution to 2x^2+2y^2+12y-2y-3=0 is Circle with (a,b)=(0,-5/2),r=(sqrt(31))/2

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2x^2+2y^2+12y-2y-3=0

2 x^{2} + 2 y^{2} + 12 y - 2 y - 3 = 0

(a, b) = (0, - \frac{5}{2}), r = \frac{31}{2}

Solution steps

2 x^{2} + 2 y^{2} + 12 y - 2 y - 3 = 0

Rewrite

2 x^{2} + 2 y^{2} + 12 y - 2 y - 3 = 0

in the form of the standard circle equation

(x - 0)^{2} + (y - (- \frac{5}{2}))^{2} = (\frac{31}{2})^{2}

Therefore the circle properties are:

(a, b) = (0, - \frac{5}{2}), r = \frac{31}{2}

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

2 x^{2} + 6 x + 2 y^{2} + 3 y - 2 = 0

4 x^{2} + 4 y^{2} + 40 y + 75 = 0

(- x)^{2} + (- y)^{2} = 14

a^{2} + b^{2} = 52

What is 2x^2+2y^2+12y-2y-3=0 ?
The solution to 2x^2+2y^2+12y-2y-3=0 is Circle with (a,b)=(0,-5/2),r=(sqrt(31))/2