What is 4y^2+24y+4x^2-12+9=0 ?

The solution to 4y^2+24y+4x^2-12+9=0 is Circle with (a,b)=(0,-3),r=(sqrt(39))/2

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4y^2+24y+4x^2-12+9=0

4 y^{2} + 24 y + 4 x^{2} - 12 + 9 = 0

(a, b) = (0, - 3), r = \frac{39}{2}

Solution steps

4 y^{2} + 24 y + 4 x^{2} - 12 + 9 = 0

Rewrite

4 y^{2} + 24 y + 4 x^{2} - 12 + 9 = 0

in the form of the standard circle equation

(x - 0)^{2} + (y - (- 3))^{2} = (\frac{39}{2})^{2}

Therefore the circle properties are:

(a, b) = (0, - 3), r = \frac{39}{2}

(x + 8)^{2} + (y - 6)^{2} = 100

2 x^{2} + 2 y^{2} + 6 x - 8 y - 3 = 0

3 0^{2} = a^{2} + b^{2}

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

(x + π)^{2} + (y - 2 π)^{2} = 8

What is 4y^2+24y+4x^2-12+9=0 ?
The solution to 4y^2+24y+4x^2-12+9=0 is Circle with (a,b)=(0,-3),r=(sqrt(39))/2