What is x^{(2)}+y^{(2)}+25x+10y=-12 ?

The solution to x^{(2)}+y^{(2)}+25x+10y=-12 is Circle with (a,b)=(-25/2 ,-5),r=(sqrt(677))/2

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x^{(2)}+y^{(2)}+25x+10y=-12

x^{(2)} + y^{(2)} + 25 x + 10 y = - 12

(a, b) = (- \frac{25}{2}, - 5), r = \frac{677}{2}

Solution steps

x^{2} + y^{2} + 25 x + 10 y = - 12

Rewrite

x^{2} + y^{2} + 25 x + 10 y = - 12

in the form of the standard circle equation

(x - (- \frac{25}{2}))^{2} + (y - (- 5))^{2} = (\frac{677}{2})^{2}

Therefore the circle properties are:

(a, b) = (- \frac{25}{2}, - 5), r = \frac{677}{2}

x^{2} + y^{2} + 14 x - 20 y + 100 = 0

x^{2} + 6 x + y^{2} - 8 y - 75 = 0

(x + 2)^{2} + (y + 8)^{2} = 100

(x + 1)^{2} + (y + 2)^{2} = 1

(x - 2)^{2} + (y - 0)^{2} = 5^{2}

What is x^{(2)}+y^{(2)}+25x+10y=-12 ?
The solution to x^{(2)}+y^{(2)}+25x+10y=-12 is Circle with (a,b)=(-25/2 ,-5),r=(sqrt(677))/2