cancel
Showing results for
Did you mean:
cancel
Showing results for
Did you mean:

SOLVED
Highlighted
Emerald IV

## Cone, plane, ellipse

I know a and b of an ellipse. What is the value alpha of a circular cone?

1 ACCEPTED SOLUTION

Accepted Solutions
Highlighted

## Re: Cone, plane, ellipse

Yes,

here is example when a=15, b=8 and alpha=30 degree...

..and when alpha changes to 40 degree

Observe that auxiliary view is normal to cutting plane and does not show real cone angle.

11 REPLIES 11
Highlighted

## Re: Cone, plane, ellipse

a & b are not sufficient to define alpha.

No mather what alpha you have, you can allways slice cone to obtain ellipse with dimmensions a & b.

/Avdo

Highlighted

## Re: Cone, plane, ellipse

Thanks!

For a of a circular cone too?

Highlighted

## Re: Cone, plane, ellipse

Yes,

here is example when a=15, b=8 and alpha=30 degree...

..and when alpha changes to 40 degree

Observe that auxiliary view is normal to cutting plane and does not show real cone angle.

## Re: Cone, plane, ellipse

Thanks!

I suspected it. But I always want to check!

When I was in school, I drew something around 1000 triangles, measured their angles and made sure that their sum is 200 degrees.

Just kidding! 180 degrees!

Highlighted

## Re: Cone, plane, ellipse

Nice,

Now: is it possible to prove, or dis-prove, that one of the two focal points of the ellipse lies on the axis of the cone?

Luc

Highlighted

## Re: Cone, plane, ellipse

Fine idea!

One of the two focal points of the ellipse lies on the axis of the cone.

PS

New year tree for our problem

Highlighted

## Re: Cone, plane, ellipse

@ValeryOchkov wrote:

Fine idea!

One of the two focal points of the ellipse lies on the axis of the cone.

Mission impossible (if we still are talking about a circular cone).

The focal points are where the Dandelin spheres touch the plane.

Highlighted

## Re: Cone, plane, ellipse

Theoretically there is one trivial solution to the problem!

One focus is on the axis if other focus is on axis too 🙂 lol

observe that circle is only special variant of the ellipse when a=b=r

otherwise it is allways offset from cone axis to the focal points.

/Avdo

Highlighted

## Re: Cone, plane, ellipse

@ptc-5737066 wrote:

...

otherwise it is allways offset from cone axis to the focal points.

Which needs to be proved.

One way to do so is by the Dandelin spheres - if of them should touch the plane in a point on the axis, the plane has to be horizontal and the intersection is a circle.

You sure know that the center of the ellipse is not on the axis as well (unless in the case of a circle).

Announcements