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=5

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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 = 5

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} = 5^{2}

Therefore the circle properties are:

(a, b) = (- 2, 3), r = 5

x, x^{2} + Y (x)^{2} = 4

2 x^{2} + 2 y^{2} + 4 x - 3 y = - 2

x^{2} - 4 x + y^{2} + 4 y = 1

3 y^{2} + 3 x^{2} - 27 = 0

9 x^{2} - 36 x + 9 y^{2} + 6 y = - 28

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=5