What is 3x^2+3y^2-27x-9y-24=0 ?

The solution to 3x^2+3y^2-27x-9y-24=0 is Circle with (a,b)=(9/2 , 3/2),r=sqrt(61/2)

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3x^2+3y^2-27x-9y-24=0

3 x^{2} + 3 y^{2} - 27 x - 9 y - 24 = 0

(a, b) = (\frac{9}{2}, \frac{3}{2}), r = \frac{61}{2}

Solution steps

3 x^{2} + 3 y^{2} - 27 x - 9 y - 24 = 0

Rewrite

3 x^{2} + 3 y^{2} - 27 x - 9 y - 24 = 0

in the form of the standard circle equation

(x - \frac{9}{2})^{2} + (y - \frac{3}{2})^{2} = (\frac{61}{2})^{2}

Therefore the circle properties are:

(a, b) = (\frac{9}{2}, \frac{3}{2}), r = \frac{61}{2}

x^{2} + y^{2} + 2 x - 3 y - 15 = 0

x^{2} + y^{2} - 22 x + 6 y + 129 = 0

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

2 x^{2} + 2 y^{2} + 44 x + 28 y = 52

x^{2} + (y - 8)^{2} = 5

What is 3x^2+3y^2-27x-9y-24=0 ?
The solution to 3x^2+3y^2-27x-9y-24=0 is Circle with (a,b)=(9/2 , 3/2),r=sqrt(61/2)