What is 2x^2+2y^2+10x+12y=-12 ?

The solution to 2x^2+2y^2+10x+12y=-12 is Circle with (a,b)=(-5/2 ,-3),r=(sqrt(37))/2

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2x^2+2y^2+10x+12y=-12

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

(a, b) = (- \frac{5}{2}, - 3), r = \frac{37}{2}

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - (- \frac{5}{2}))^{2} + (y - (- 3))^{2} = (\frac{37}{2})^{2}

Therefore the circle properties are:

(a, b) = (- \frac{5}{2}, - 3), r = \frac{37}{2}

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

(x - 3)^{2} + (y - 2)^{2} = 49

(x + 4)^{2} + (y - 6)^{2} = 48

(x - 9)^{2} + y^{2} = 81

x^{2} + y^{2} + 6 x + 5 y = \frac{- 45}{4}

What is 2x^2+2y^2+10x+12y=-12 ?
The solution to 2x^2+2y^2+10x+12y=-12 is Circle with (a,b)=(-5/2 ,-3),r=(sqrt(37))/2