What is 2x^2+2y^2+10x-2y=7 ?

The solution to 2x^2+2y^2+10x-2y=7 is Circle with (a,b)=(-5/2 , 1/2),r=sqrt(10)

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

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

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

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

(x - (- 5))^{2} + (y - 7)^{2} = (11)^{2}

x^{2} + y^{2} + 10 x - 8 y + 36 = 0

(x - 1)^{2} + (y + 11)^{2} + (0 - 8)^{2} = 100

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

122 = a^{2} + b^{2}

What is 2x^2+2y^2+10x-2y=7 ?
The solution to 2x^2+2y^2+10x-2y=7 is Circle with (a,b)=(-5/2 , 1/2),r=sqrt(10)