What is 2x^2-8x+2y^2+12y+14=0 ?

The solution to 2x^2-8x+2y^2+12y+14=0 is Circle with (a,b)=(2,-3),r=sqrt(6)

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2x^2-8x+2y^2+12y+14=0

2 x^{2} - 8 x + 2 y^{2} + 12 y + 14 = 0

(a, b) = (2, - 3), r = 6

Solution steps

2 x^{2} - 8 x + 2 y^{2} + 12 y + 14 = 0

Rewrite

2 x^{2} - 8 x + 2 y^{2} + 12 y + 14 = 0

in the form of the standard circle equation

(x - 2)^{2} + (y - (- 3))^{2} = (6)^{2}

Therefore the circle properties are:

(a, b) = (2, - 3), r = 6

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

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

x^{2} = 25 - y^{2}

x^{2} + 12 x + y^{2} - 8 y + 3 = 0

x^{2} + y^{2} - 4 x + 6 y - 2 = 0

What is 2x^2-8x+2y^2+12y+14=0 ?
The solution to 2x^2-8x+2y^2+12y+14=0 is Circle with (a,b)=(2,-3),r=sqrt(6)