What is 6x^2+6y^2+12x+9y-54=0 ?

The solution to 6x^2+6y^2+12x+9y-54=0 is Circle with (a,b)=(-1,-3/4),r= 13/4

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6x^2+6y^2+12x+9y-54=0

6 x^{2} + 6 y^{2} + 12 x + 9 y - 54 = 0

(a, b) = (- 1, - \frac{3}{4}), r = \frac{13}{4}

Solution steps

6 x^{2} + 6 y^{2} + 12 x + 9 y - 54 = 0

Rewrite

6 x^{2} + 6 y^{2} + 12 x + 9 y - 54 = 0

in the form of the standard circle equation

(x - (- 1))^{2} + (y - (- \frac{3}{4}))^{2} = (\frac{13}{4})^{2}

Therefore the circle properties are:

(a, b) = (- 1, - \frac{3}{4}), r = \frac{13}{4}

(x + 3)^{2} + (y - 2)^{2} = 81

144 x^{2} + 144 y^{2} - 96 x + 72 y - 11 = 0

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

x^{2} + y^{2} - x - 10 y + 5 = 0

x^{2} + y^{2} + 5 x - 10 y - 5 = 0

What is 6x^2+6y^2+12x+9y-54=0 ?
The solution to 6x^2+6y^2+12x+9y-54=0 is Circle with (a,b)=(-1,-3/4),r= 13/4