What is x^{(2)}+y^{(2)}+4x-6y+12=0 ?

The solution to x^{(2)}+y^{(2)}+4x-6y+12=0 is Circle with (a,b)=(-2,3),r=1

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x^{(2)}+y^{(2)}+4x-6y+12=0

x^{(2)} + y^{(2)} + 4 x - 6 y + 12 = 0

(a, b) = (- 2, 3), r = 1

Solution steps

x^{2} + y^{2} + 4 x - 6 y + 12 = 0

Rewrite

x^{2} + y^{2} + 4 x - 6 y + 12 = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (- 2, 3), r = 1

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

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

x^{2} + y^{2} - x - 2 y - 1 = 0

x (x + 5) + (y - 2)^{2} = 0

(x + 3)^{2} + (y - 3)^{2} = 25

What is x^{(2)}+y^{(2)}+4x-6y+12=0 ?
The solution to x^{(2)}+y^{(2)}+4x-6y+12=0 is Circle with (a,b)=(-2,3),r=1