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

The solution to 2x^2+2y^2-2x+6y=45 is Circle with (a,b)=(1/2 ,-3/2),r=5

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard circle equation

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

Therefore the circle properties are:

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

9 x^{2} + 9 y^{2} - 6 x + 24 y = 19

2 x^{2} + 2 y^{2} + 12 x - 2 y - 3 = 0

x^{2} + y^{2} + 8 x - 9 y = 6

2 x^{2} + 2 y^{2} - 14 x + 18 y = 7

x^{2} + y^{2} + 8 y = 3

What is 2x^2+2y^2-2x+6y=45 ?
The solution to 2x^2+2y^2-2x+6y=45 is Circle with (a,b)=(1/2 ,-3/2),r=5