What is 3x^2+3y^2-9x+27y=5 ?

The solution to 3x^2+3y^2-9x+27y=5 is Circle with (a,b)=(3/2 ,-9/2),r=sqrt(145/6)

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3x^2+3y^2-9x+27y=5

3 x^{2} + 3 y^{2} - 9 x + 27 y = 5

(a, b) = (\frac{3}{2}, - \frac{9}{2}), r = \frac{145}{6}

Solution steps

3 x^{2} + 3 y^{2} - 9 x + 27 y = 5

Rewrite

3 x^{2} + 3 y^{2} - 9 x + 27 y = 5

in the form of the standard circle equation

(x - \frac{3}{2})^{2} + (y - (- \frac{9}{2}))^{2} = (\frac{145}{6})^{2}

Therefore the circle properties are:

(a, b) = (\frac{3}{2}, - \frac{9}{2}), r = \frac{145}{6}

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

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What is 3x^2+3y^2-9x+27y=5 ?
The solution to 3x^2+3y^2-9x+27y=5 is Circle with (a,b)=(3/2 ,-9/2),r=sqrt(145/6)