Re: [EMHL] A line and a conic
- Dear friends,
This brings me to a new problem.
I never got into this.
Given an equation f(x,y,z).
How to convert it to a point in time (t): (x(t) : y(t) : z(t))?
To make it visual and more appealing. When we have a conical orbit of a planet or comet.
How can we describe its location as a function of time in barycentric coordinates ?
Chris van Tienhoven
--- In Hyacinthos@yahoogroups.com, Barry Wolk <wolkbarry@...> wrote:
> > Dear friends
> > if we know the line
> > Px + Qy + Rz = 0
> > and the conic
> > fxx + gyy + hzz + 2pyz + 2qzx + 2rxy = 0
> > is there a formula giving the barycentric
> > coordinates of their intersection points?
> > Best regards
> > Nikos Dergiades
> There were several replies, including asking for cyclically symmetric coordinates for those intersection points.
> The points on the line Px+Qy+Rz=0 can be parametrized as
> (x, y, z)=((Q-R)(QR+t), (R-P)(RP+t), (P-Q)(PQ+t))
> Substitute these formulas for x,y,z into the equation of the conic, to get a cyclically symmetric quadratic equation for the parameter t. Its two roots will give the intersection points in the requested form.
> Barry Wolk