What is 4x^2+4y^2-4x+24y+1=0 ?

The solution to 4x^2+4y^2-4x+24y+1=0 is Circle with (a,b)=(1/2 ,-3),r=3

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4x^2+4y^2-4x+24y+1=0

4 x^{2} + 4 y^{2} - 4 x + 24 y + 1 = 0

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

Solution steps

4 x^{2} + 4 y^{2} - 4 x + 24 y + 1 = 0

Rewrite

4 x^{2} + 4 y^{2} - 4 x + 24 y + 1 = 0

in the form of the standard circle equation

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

Therefore the circle properties are:

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

(x - 4)^{2} + (y - 7)^{2} = 49

9 x^{2} + 9 y^{2} - 42 x + 84 y + 65 = 0

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

2 x^{2} + 8 x + 2 y^{2} - 16 y - 5 = 0

x^{2} + y^{2} + 8 x - 12 y + 27 = 0

What is 4x^2+4y^2-4x+24y+1=0 ?
The solution to 4x^2+4y^2-4x+24y+1=0 is Circle with (a,b)=(1/2 ,-3),r=3