What is x^2+5x+y^2-y= 5/2 ?

The solution to x^2+5x+y^2-y= 5/2 is Circle with (a,b)=(-5/2 , 1/2),r=3

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x^2+5x+y^2-y= 5/2

x^{2} + 5 x + y^{2} - y = \frac{5}{2}

(a, b) = (- \frac{5}{2}, \frac{1}{2}), r = 3

Solution steps

x^{2} + 5 x + y^{2} - y = \frac{5}{2}

Rewrite

x^{2} + 5 x + y^{2} - y = \frac{5}{2}

in the form of the standard circle equation

(x - (- \frac{5}{2}))^{2} + (y - \frac{1}{2})^{2} = 3^{2}

Therefore the circle properties are:

(a, b) = (- \frac{5}{2}, \frac{1}{2}), r = 3

(x - 1)^{2} + (y - 4)^{2} = 10

(x - 1)^{2} + (y - 4)^{2} = 17

(x - 5)^{2} + (y + 3)^{2} = 36

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

x^{2} + y^{2} + 6 y - 1 = 0

What is x^2+5x+y^2-y= 5/2 ?
The solution to x^2+5x+y^2-y= 5/2 is Circle with (a,b)=(-5/2 , 1/2),r=3