What is the center 2x^2-6x+2y^2+2y=45 ?

The center 2x^2-6x+2y^2+2y=45 is (3/2 ,-1/2)

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center 2x^2-6x+2y^2+2y=45

center

2 x^{2} - 6 x + 2 y^{2} + 2 y = 45

(\frac{3}{2}, - \frac{1}{2})

Solution steps

2 x^{2} - 6 x + 2 y^{2} + 2 y = 45

Rewrite

2 x^{2} - 6 x + 2 y^{2} + 2 y = 45

in the form of the standard circle equation

(x - \frac{3}{2})^{2} + (y - (- \frac{1}{2}))^{2} = 5^{2}

Therefore the circle properties are:

(a, b) = (\frac{3}{2}, - \frac{1}{2}), r = 5

And the center is:

(\frac{3}{2}, - \frac{1}{2})

x^{2} + y^{2} - 2 x - 6 y - 15 = 0

x^{2} + 24 x + y^{2} + 10 y = - 160

(x + 2)^{2} + (y - 3)^{2} = 16

x^{2} + y^{2} + 14 x - 16 y + 64 = 0

2 x^{2} - 2 x + 2 y^{2} + 4 y = - 1

What is the center 2x^2-6x+2y^2+2y=45 ?
The center 2x^2-6x+2y^2+2y=45 is (3/2 ,-1/2)