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

The solution to 4x^2-4+4y^2+4y=9 is Circle with (a,b)=(0,-1/2),r=sqrt(7/2)

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

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

(a, b) = (0, - \frac{1}{2}), r = \frac{7}{2}

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - 0)^{2} + (y - (- \frac{1}{2}))^{2} = (\frac{7}{2})^{2}

Therefore the circle properties are:

(a, b) = (0, - \frac{1}{2}), r = \frac{7}{2}

x^{2} + y^{2} - \frac{3}{2} x + \frac{2}{3} y - \frac{239}{36} = 0

[x - (- 3)]^{2} + (y - 1)^{2} = 1 0^{2}

x^{2} + y^{2} + 18 x = - 80

x^{2} + y^{2} > \frac{1}{2}

x^{2} - 8 x + y^{2} - 4 y + 10 = 0

What is 4x^2-4+4y^2+4y=9 ?
The solution to 4x^2-4+4y^2+4y=9 is Circle with (a,b)=(0,-1/2),r=sqrt(7/2)