What is 2x^2+2y^2+6x-8y=-12 ?

The solution to 2x^2+2y^2+6x-8y=-12 is Circle with (a,b)=(-3/2 ,2),r= 1/2

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2x^2+2y^2+6x-8y=-12

2 x^{2} + 2 y^{2} + 6 x - 8 y = - 12

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

Solution steps

2 x^{2} + 2 y^{2} + 6 x - 8 y = - 12

Rewrite

2 x^{2} + 2 y^{2} + 6 x - 8 y = - 12

in the form of the standard circle equation

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

Therefore the circle properties are:

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

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

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

x^{2} + y^{2} + 3 x - 6 y + 9 = 0

x^{2} + y^{2} + 6 x + 18 y + 9 = 0

x^{2} + y^{2} + 8 x + 7 = 0

What is 2x^2+2y^2+6x-8y=-12 ?
The solution to 2x^2+2y^2+6x-8y=-12 is Circle with (a,b)=(-3/2 ,2),r= 1/2