What is the center 2x^2+2y^2+10x=2y+7 ?

The center 2x^2+2y^2+10x=2y+7 is (-5/2 , 1/2)

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center 2x^2+2y^2+10x=2y+7

center

2 x^{2} + 2 y^{2} + 10 x = 2 y + 7

(- \frac{5}{2}, \frac{1}{2})

Solution steps

2 x^{2} + 2 y^{2} + 10 x = 2 y + 7

Rewrite

2 x^{2} + 2 y^{2} + 10 x = 2 y + 7

in the form of the standard circle equation

(x - (- \frac{5}{2}))^{2} + (y - \frac{1}{2})^{2} = (10)^{2}

Therefore the circle properties are:

(a, b) = (- \frac{5}{2}, \frac{1}{2}), r = 10

And the center is:

(- \frac{5}{2}, \frac{1}{2})

(x - 2)^{2} + (y + 4)^{2} = 25

x^{2} + y^{2} - 4 x - 8 y - 5 = 0

x^{2} + (y - 5)^{2} = 36

x^{2} + y^{2} + 12 x - 12 y + 36 = 0

x^{2} + (y - 5)^{2} = 16

What is the center 2x^2+2y^2+10x=2y+7 ?
The center 2x^2+2y^2+10x=2y+7 is (-5/2 , 1/2)