What is x^2+y^2+6x-8y+12=0 ?

The solution to x^2+y^2+6x-8y+12=0 is Circle with (a,b)=(-3,4),r=sqrt(13)

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x^2+y^2+6x-8y+12=0

x^{2} + y^{2} + 6 x - 8 y + 12 = 0

(a, b) = (- 3, 4), r = 13

Solution steps

x^{2} + y^{2} + 6 x - 8 y + 12 = 0

Rewrite

x^{2} + y^{2} + 6 x - 8 y + 12 = 0

in the form of the standard circle equation

(x - (- 3))^{2} + (y - 4)^{2} = (13)^{2}

Therefore the circle properties are:

(a, b) = (- 3, 4), r = 13

4 (x^{2} - 2 x + 1) + 4 (y^{2} - y + 0) = 11 + 1 + 0

x^{2} + y^{2} + x + y = 85 - 7

x^{2} + y^{2} - 10 x + 12 y - 83 - 0 = 0

2 x^{2} + 2 y^{2} - 12 x + 8 y + 24 = 0

x^{2} + y^{2} - 8 x - 14 y - 7 = 0

What is x^2+y^2+6x-8y+12=0 ?
The solution to x^2+y^2+6x-8y+12=0 is Circle with (a,b)=(-3,4),r=sqrt(13)