What is 4x^2-4x+4y^2+4y=9 ?

The solution to 4x^2-4x+4y^2+4y=9 is Circle with (a,b)=(1/2 ,-1/2),r=(sqrt(11))/2

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4x^2-4x+4y^2+4y=9

4 x^{2} - 4 x + 4 y^{2} + 4 y = 9

(a, b) = (\frac{1}{2}, - \frac{1}{2}), r = \frac{11}{2}

Solution steps

4 x^{2} - 4 x + 4 y^{2} + 4 y = 9

Rewrite

4 x^{2} - 4 x + 4 y^{2} + 4 y = 9

in the form of the standard circle equation

(x - \frac{1}{2})^{2} + (y - (- \frac{1}{2}))^{2} = (\frac{11}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - \frac{1}{2}), r = \frac{11}{2}

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

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

4 x^{2} + 4 y^{2} + 40 x - 32 y - 5 = 0

4 x^{2} + 4 y^{2} - 20 x + 40 y = - 5

4 x^{2} + 4 y^{2} + 6 x + 8 y - 5 = 0

What is 4x^2-4x+4y^2+4y=9 ?
The solution to 4x^2-4x+4y^2+4y=9 is Circle with (a,b)=(1/2 ,-1/2),r=(sqrt(11))/2