What is 2x^2-14x+2y^2+12y=-21/2 ?

The solution to 2x^2-14x+2y^2+12y=-21/2 is Circle with (a,b)=(7/2 ,-3),r=4

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2x^2-14x+2y^2+12y=-21/2

2 x^{2} - 14 x + 2 y^{2} + 12 y = - \frac{21}{2}

(a, b) = (\frac{7}{2}, - 3), r = 4

Solution steps

2 x^{2} - 14 x + 2 y^{2} + 12 y = - \frac{21}{2}

Rewrite

2 x^{2} - 14 x + 2 y^{2} + 12 y = - \frac{21}{2}

in the form of the standard circle equation

(x - \frac{7}{2})^{2} + (y - (- 3))^{2} = 4^{2}

Therefore the circle properties are:

(a, b) = (\frac{7}{2}, - 3), r = 4

(x - 1)^{2} + (y + 5)^{2} \leq 4

(x - 3)^{2} + (y + 11)^{2} = 75

x^{2} - 2 x + y^{2} + 4 y - 11 = 0

(x - 9)^{2} + y^{2} = 32

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

What is 2x^2-14x+2y^2+12y=-21/2 ?
The solution to 2x^2-14x+2y^2+12y=-21/2 is Circle with (a,b)=(7/2 ,-3),r=4