What is x^2-4x+6y+y^2=4 ?

The solution to x^2-4x+6y+y^2=4 is Circle with (a,b)=(2,-3),r=sqrt(17)

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x^2-4x+6y+y^2=4

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

(a, b) = (2, - 3), r = 17

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - 2)^{2} + (y - (- 3))^{2} = (17)^{2}

Therefore the circle properties are:

(a, b) = (2, - 3), r = 17

x^{2} + y^{2} + 6 x + 8 y + 24 = 0

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

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

x^{2} + (y + 2)^{2} = 36

(x + 5)^{2} + (y + 4)^{2} = 9

What is x^2-4x+6y+y^2=4 ?
The solution to x^2-4x+6y+y^2=4 is Circle with (a,b)=(2,-3),r=sqrt(17)