Given an infinite double cone of the form $ax^2+by^2+cz^2+dxy+exz+fyz=0$, how can I get the slope of the double cone, the radius at a given height along the cone's axis, and the angles of rotation?
For example:
Given $2x^2+2y^2-0.5z^2=0$ (visualization):
- the radius at the height $-1$ is $0.5$
- the slope is $\pm2$
- the angles of rotation are $0$ and $0$ (unrotated)
Note that the radius-at-height and slope attributes must be as if the cone were not rotated. For example:
Given $2x^2+2y^2-0.5z^2-xz=0$ (visualization):
- the radius at the height $-1$ is $0.5$
- the slope is $\pm2$
- the angles of rotation are $0$ and $\sim\frac{\pi}{6}$ (the second is visually observed)
How can I solve for the various attributes algebraically?