What is 9x^2+12x+9y^2-18y-23=0 ?

The solution to 9x^2+12x+9y^2-18y-23=0 is Circle with (a,b)=(-2/3 ,1),r=2

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9x^2+12x+9y^2-18y-23=0

9 x^{2} + 12 x + 9 y^{2} - 18 y - 23 = 0

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

Solution steps

9 x^{2} + 12 x + 9 y^{2} - 18 y - 23 = 0

Rewrite

9 x^{2} + 12 x + 9 y^{2} - 18 y - 23 = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

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

x^{2} + y^{2} = 12

x^{2} - 4 x + y^{2} - 4 y - 8 = 0

x^{2} + y^{2} < 4

x^{2} + y^{2} = 2 x

x^{2} + 8 x + y^{2} + 2 y + 8 = 0

What is 9x^2+12x+9y^2-18y-23=0 ?
The solution to 9x^2+12x+9y^2-18y-23=0 is Circle with (a,b)=(-2/3 ,1),r=2