What is 36x^2-36x+36y^2+72y=279 ?

The solution to 36x^2-36x+36y^2+72y=279 is Circle with (a,b)=(1/2 ,-1),r=3

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36x^2-36x+36y^2+72y=279

36 x^{2} - 36 x + 36 y^{2} + 72 y = 279

(a, b) = (\frac{1}{2}, - 1), r = 3

Solution steps

36 x^{2} - 36 x + 36 y^{2} + 72 y = 279

Rewrite

36 x^{2} - 36 x + 36 y^{2} + 72 y = 279

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (\frac{1}{2}, - 1), r = 3

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

(x + 4)^{2} + (y - 4)^{2} = 9

(x - 3)^{2} + (y + 4)^{2} = 25

x^{2} - 3 x + y^{2} + 1 = 0

x^{2} + y^{2} + 4 x - 10 y - 7 = 0

What is 36x^2-36x+36y^2+72y=279 ?
The solution to 36x^2-36x+36y^2+72y=279 is Circle with (a,b)=(1/2 ,-1),r=3