What is 2x^2-12x+2y^2+6y= 19/2 ?

The solution to 2x^2-12x+2y^2+6y= 19/2 is Circle with (a,b)=(3,-3/2),r=4

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2x^2-12x+2y^2+6y= 19/2

2 x^{2} - 12 x + 2 y^{2} + 6 y = \frac{19}{2}

(a, b) = (3, - \frac{3}{2}), r = 4

Solution steps

2 x^{2} - 12 x + 2 y^{2} + 6 y = \frac{19}{2}

Rewrite

2 x^{2} - 12 x + 2 y^{2} + 6 y = \frac{19}{2}

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (3, - \frac{3}{2}), r = 4

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

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

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

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

(X - 4)^{2} + (Y + 3)^{2} = 1

What is 2x^2-12x+2y^2+6y= 19/2 ?
The solution to 2x^2-12x+2y^2+6y= 19/2 is Circle with (a,b)=(3,-3/2),r=4