What is 4x^2+36x+4y^2-8y+68=x^2-6x+y^2-4y+13 ?

The solution to 4x^2+36x+4y^2-8y+68=x^2-6x+y^2-4y+13 is Circle with (a,b)=(-7, 2/3),r=(2sqrt(70))/3

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4x^2+36x+4y^2-8y+68=x^2-6x+y^2-4y+13

4 x^{2} + 36 x + 4 y^{2} - 8 y + 68 = x^{2} - 6 x + y^{2} - 4 y + 13

(a, b) = (- 7, \frac{2}{3}), r = \frac{2 70}{3}

Solution steps

4 x^{2} + 36 x + 4 y^{2} - 8 y + 68 = x^{2} - 6 x + y^{2} - 4 y + 13

Rewrite

4 x^{2} + 36 x + 4 y^{2} - 8 y + 68 = x^{2} - 6 x + y^{2} - 4 y + 13

in the form of the standard circle equation

(x - (- 7))^{2} + (y - \frac{2}{3})^{2} = (\frac{2 70}{3})^{2}

Therefore the circle properties are:

(a, b) = (- 7, \frac{2}{3}), r = \frac{2 70}{3}

x^{2} + (y - 1)^{2} = 16

(x^{2} - 10 x + 25) + (y^{2} + 4 y + 4) = 36

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

x^{2} + y^{2} - 6 x + 12 y + 41 = 0

(\frac{x - 19}{4})^{2} + (\frac{y - 9}{4})^{2} = 17

What is 4x^2+36x+4y^2-8y+68=x^2-6x+y^2-4y+13 ?
The solution to 4x^2+36x+4y^2-8y+68=x^2-6x+y^2-4y+13 is Circle with (a,b)=(-7, 2/3),r=(2sqrt(70))/3