What is 3x^2+3y^2-2x+y-6=0 ?

The solution to 3x^2+3y^2-2x+y-6=0 is Circle with (a,b)=(1/3 ,-1/6),r=(sqrt(77))/6

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3x^2+3y^2-2x+y-6=0

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

(a, b) = (\frac{1}{3}, - \frac{1}{6}), r = \frac{77}{6}

Solution steps

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

Rewrite

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

in the form of the standard circle equation

(x - \frac{1}{3})^{2} + (y - (- \frac{1}{6}))^{2} = (\frac{77}{6})^{2}

Therefore the circle properties are:

(a, b) = (\frac{1}{3}, - \frac{1}{6}), r = \frac{77}{6}

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

x^{2} + y^{2} - 6 x + 4 y - 12 = 0

x^{2} + y^{2} + 2 x + 2 y - 7 = 0

4 x^{2} + 4 y^{2} - 56 x + 8 y + 56 = 0

x^{2} + (y - 2)^{2} = 28

What is 3x^2+3y^2-2x+y-6=0 ?
The solution to 3x^2+3y^2-2x+y-6=0 is Circle with (a,b)=(1/3 ,-1/6),r=(sqrt(77))/6