What is y^{(2)}+4x-3+x^{(2)}+6y=0 ?

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

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y^{(2)}+4x-3+x^{(2)}+6y=0

y^{(2)} + 4 x - 3 + x^{(2)} + 6 y = 0

(a, b) = (- 2, - 3), r = 4

Solution steps

y^{2} + 4 x - 3 + x^{2} + 6 y = 0

Rewrite

y^{2} + 4 x - 3 + x^{2} + 6 y = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (- 2, - 3), r = 4

(x - 5)^{2} + (y - 3)^{2} = 9

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

x^{2} + y^{2} - 6 x - 8 y - 4 = 0

x^{2} + y^{2} - 2 x \leq 1

x^{2} + y^{2} - 2 x \leq 0

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