Re: Intersection of Ellipsoid and a Plane in space

On May 28, 2:31 pm, Mariano Suárez-Alvarez
<mariano.suarezalva...@xxxxxxxxx> wrote:
On May 28, 9:26 am, miki <miki.li...@xxxxxxxxx> wrote:





Hello All,

Can any one come up with a closed-form to the following problem...

This is a symmetrical Ellipsoid

x^2+y^2    z^2
----------- + ----- = 1
   a^2       b^2

This is a general equation for a plane in space which pass through the
origin

Ax+By+Cz=0

My question is what is the equation of the two dimensional Ellipse
which is being created
by the intersection of the Ellipsoid and the plane.

I got something of the form

x^2       y^2    r^2 * x*y
------- + ----- + ------------  = 1
s^2       t^2         p^2

where s,t,r,p are some constants.

Notice that this is not the equation of the intersection
of the ellipse and the plane, because in R^3
this is the equation of a *surface*. At most, this is
the equation of the projection of that intersection
to the x-y plane.

The problem is, I dont get an Ellipse in its known form.

You have not told us what is the `known form'.

What can I do?

Find out of what the general equation of an ellipse is.

-- m- Hide quoted text -

- Show quoted text -

Sorry,
The general form I'm looking for is

x^2 y^2
--- + --- = 1
v^2 w^2

Actually, what I'm looking for is v and w.

Thanks


.

Relevant Pages