What is x^{(2)}+y^{(2)}+4x+6y-23=0 ?

The solution to x^{(2)}+y^{(2)}+4x+6y-23=0 is Circle with (a,b)=(-2,-3),r=6

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x^{(2)}+y^{(2)}+4x+6y-23=0

x^{(2)} + y^{(2)} + 4 x + 6 y - 23 = 0

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

Solution steps

x^{2} + y^{2} + 4 x + 6 y - 23 = 0

Rewrite

x^{2} + y^{2} + 4 x + 6 y - 23 = 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} + x^{2} - 12 x = 0

3 x^{2} + 3 y^{2} - 12 x - 15 y - 6 = 0

x^{2} + y^{2} - \frac{27}{8} x + \frac{31}{8} y - \frac{39}{8} = 0

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

x^{2} + y^{2} \leq 12

What is x^{(2)}+y^{(2)}+4x+6y-23=0 ?
The solution to x^{(2)}+y^{(2)}+4x+6y-23=0 is Circle with (a,b)=(-2,-3),r=6