What is 9x^2+9y^2+54x-36y=-17 ?

The solution to 9x^2+9y^2+54x-36y=-17 is Circle with (a,b)=(-3,2),r= 10/3

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9x^2+9y^2+54x-36y=-17

9 x^{2} + 9 y^{2} + 54 x - 36 y = - 17

(a, b) = (- 3, 2), r = \frac{10}{3}

Solution steps

9 x^{2} + 9 y^{2} + 54 x - 36 y = - 17

Rewrite

9 x^{2} + 9 y^{2} + 54 x - 36 y = - 17

in the form of the standard circle equation

(x - (- 3))^{2} + (y - 2)^{2} = (\frac{10}{3})^{2}

Therefore the circle properties are:

(a, b) = (- 3, 2), r = \frac{10}{3}

x^{2} + (y + 6)^{2} = 8

x^{2} + y^{2} = 8 (x + y) + 4

x^{2} + y^{2} + 4 x - 12 y + 24 = 0

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

8 x + x^{2} - 2 y = 64 - y^{2}

What is 9x^2+9y^2+54x-36y=-17 ?
The solution to 9x^2+9y^2+54x-36y=-17 is Circle with (a,b)=(-3,2),r= 10/3