What is -x^2-6x=z^2+2z+1 ?

The solution to -x^2-6x=z^2+2z+1 is Circle with (a,b)=(-3,-1),r=3

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-x^2-6x=z^2+2z+1

- x^{2} - 6 x = z^{2} + 2 z + 1

(a, b) = (- 3, - 1), r = 3

Solution steps

- x^{2} - 6 x = z^{2} + 2 z + 1

Rewrite

- x^{2} - 6 x = z^{2} + 2 z + 1

in the form of the standard circle equation

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

Therefore the circle properties are:

(a, b) = (- 3, - 1), r = 3

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

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

x^{2} + y^{2} + 20 x - 6 y = - 108

4 (x + 8)^{2} + 4 (y + 1)^{2} = 16

a^{2} + b^{2} = 1044

What is -x^2-6x=z^2+2z+1 ?
The solution to -x^2-6x=z^2+2z+1 is Circle with (a,b)=(-3,-1),r=3