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

The solution to 2x^2+12x+2y^2-2y-3=0 is Circle with (a,b)=(-3, 1/2),r=(sqrt(43))/2

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

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

(a, b) = (- 3, \frac{1}{2}), r = \frac{43}{2}

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - (- 3))^{2} + (y - \frac{1}{2})^{2} = (\frac{43}{2})^{2}

Therefore the circle properties are:

(a, b) = (- 3, \frac{1}{2}), r = \frac{43}{2}

x^{2} + y^{2} + 6 x - 13 y + 13 = 0

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

5 x^{2} + 5 y^{2} + 20 x + 30 y - 310 = 0

x^{2} + y^{2} = \frac{- x - y + 2}{2}

(X + 7)^{2} + (y - 1)^{2} = 9

What is 2x^2+12x+2y^2-2y-3=0 ?
The solution to 2x^2+12x+2y^2-2y-3=0 is Circle with (a,b)=(-3, 1/2),r=(sqrt(43))/2