I need to prove, that an equation of a circle doesn't change if there's a rotation.
So, I start with $$x^2+y^2+Dx+Ey+F=0$$
and by replacing my values of $x$ and $y$ with
$$x=x'\cos\theta-y'\sin\theta$$ and $$y=x'\sin\theta+y'\cos\theta$$
which I arrive to this equation $$x'^2+y'^2+Gx'+Hy'+F=0$$
My question is, that I don't know if I have proved what I wanted to prove.