What is 9x^2+9y^2-42x+84y+65=0 ?

The solution to 9x^2+9y^2-42x+84y+65=0 is Circle with (a,b)=(7/3 ,-14/3),r=2sqrt(5)

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9x^2+9y^2-42x+84y+65=0

9 x^{2} + 9 y^{2} - 42 x + 84 y + 65 = 0

(a, b) = (\frac{7}{3}, - \frac{14}{3}), r = 25

Solution steps

9 x^{2} + 9 y^{2} - 42 x + 84 y + 65 = 0

Rewrite

9 x^{2} + 9 y^{2} - 42 x + 84 y + 65 = 0

in the form of the standard circle equation

(x - \frac{7}{3})^{2} + (y - (- \frac{14}{3}))^{2} = (25)^{2}

Therefore the circle properties are:

(a, b) = (\frac{7}{3}, - \frac{14}{3}), r = 25

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

2 x^{2} + 8 x + 2 y^{2} - 16 y - 5 = 0

x^{2} + y^{2} + 8 x - 12 y + 27 = 0

4 x^{2} + 4 y^{2} - 4 x + 2 y + 1 = 0

(x + 3)^{2} + (y - 1)^{2} = 5

What is 9x^2+9y^2-42x+84y+65=0 ?
The solution to 9x^2+9y^2-42x+84y+65=0 is Circle with (a,b)=(7/3 ,-14/3),r=2sqrt(5)