What is x^2+y^2+x+6y-55=0 ?

The solution to x^2+y^2+x+6y-55=0 is Circle with (a,b)=(-1/2 ,-3),r=(sqrt(257))/2

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x^2+y^2+x+6y-55=0

x^{2} + y^{2} + x + 6 y - 55 = 0

(a, b) = (- \frac{1}{2}, - 3), r = \frac{257}{2}

Solution steps

x^{2} + y^{2} + x + 6 y - 55 = 0

Rewrite

x^{2} + y^{2} + x + 6 y - 55 = 0

in the form of the standard circle equation

(x - (- \frac{1}{2}))^{2} + (y - (- 3))^{2} = (\frac{257}{2})^{2}

Therefore the circle properties are:

(a, b) = (- \frac{1}{2}, - 3), r = \frac{257}{2}

x^{2} + y^{2} - 8 x - 6 y - 19 = 0

(x - \frac{23}{5})^{2} + (y + \frac{2}{5})^{2} = \frac{373}{25}

(x + 3)^{2} + (y + 2)^{2} = 45

(x - 2)^{(2)} + (y - 3)^{(2)} = 7

(a + b) + (a - b) = a^{2} + b^{2}

What is x^2+y^2+x+6y-55=0 ?
The solution to x^2+y^2+x+6y-55=0 is Circle with (a,b)=(-1/2 ,-3),r=(sqrt(257))/2