What is 2x^2+16x+2y^2+14y=-77/2 ?

The solution to 2x^2+16x+2y^2+14y=-77/2 is Circle with (a,b)=(-4,-7/2),r=3

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2x^2+16x+2y^2+14y=-77/2

2 x^{2} + 16 x + 2 y^{2} + 14 y = - \frac{77}{2}

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

Solution steps

2 x^{2} + 16 x + 2 y^{2} + 14 y = - \frac{77}{2}

Rewrite

2 x^{2} + 16 x + 2 y^{2} + 14 y = - \frac{77}{2}

in the form of the standard circle equation

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

Therefore the circle properties are:

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

1^{2} = (x - 0)^{2} + (y - 0)^{2}

x^{2} + y^{2} - 4 y - 15 = 6

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

5 0^{2} = (x - 21.21)^{2} + (y - 21.21)^{2}

x^{2} + y^{2} - 4 x - 14 y + 50 = 0

What is 2x^2+16x+2y^2+14y=-77/2 ?
The solution to 2x^2+16x+2y^2+14y=-77/2 is Circle with (a,b)=(-4,-7/2),r=3