What is 4x^2-4x+4y^2+12y=6 ?

The solution to 4x^2-4x+4y^2+12y=6 is Circle with (a,b)=(1/2 ,-3/2),r=2

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4x^2-4x+4y^2+12y=6

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

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

(x - 9)^{2} + (y + 5)^{2} = 49

x^{2} + y^{2} + 16 x - 16 y + 124 = 0

(x - 1)^{2} + (y + 5)^{2} = 10

(x + 5)^{2} + (y - 4)^{2} = 9

What is 4x^2-4x+4y^2+12y=6 ?
The solution to 4x^2-4x+4y^2+12y=6 is Circle with (a,b)=(1/2 ,-3/2),r=2