What is 2x^{(2)}+2y^{(2)}-4x+12y-12=0 ?

The solution to 2x^{(2)}+2y^{(2)}-4x+12y-12=0 is Circle with (a,b)=(1,-3),r=4

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2x^{(2)}+2y^{(2)}-4x+12y-12=0

2 x^{(2)} + 2 y^{(2)} - 4 x + 12 y - 12 = 0

(a, b) = (1, - 3), r = 4

Solution steps

2 x^{2} + 2 y^{2} - 4 x + 12 y - 12 = 0

Rewrite

2 x^{2} + 2 y^{2} - 4 x + 12 y - 12 = 0

in the form of the standard circle equation

(x - 1)^{2} + (y - (- 3))^{2} = 4^{2}

Therefore the circle properties are:

(a, b) = (1, - 3), r = 4

x^{2} + y^{2} + 8 x + 8 y = - 16

3 x^{2} + 6 y + 3 y^{2} + 5 x - 15 = 0

x^{2} + y^{2} - 2 x + 4 y = 11

x^{2} + y^{2} - x + 3 y - \frac{15}{4} = 0

x^{2} + y^{2} + 6 x - 10 y - 2 = 0

What is 2x^{(2)}+2y^{(2)}-4x+12y-12=0 ?
The solution to 2x^{(2)}+2y^{(2)}-4x+12y-12=0 is Circle with (a,b)=(1,-3),r=4