• Oct 6th 2008, 05:29 PM
alexanderl33

A plane intersects a double-napped cone so that it makes an angle of 41o with the central axis. The conic form is an ellipse. The vertex angle of the cone must be less than . . .
• Oct 6th 2008, 07:28 PM
Soroban
Hello, alexanderl33!;198760]

Quote:

A plane intersects a double-napped cone and makes a 41° angle with the central axis.
The conic formed is an ellipse. The vertex angle of the cone must be less than . . .

Consider a cone with an 82° vertex angle.
The configuration looks like this.
Code:

```              *             /|\             / | \           /  |  \           /41°|41°\  /         /    |    \ /         /    |    *       /      |    / \       /      |41°/  \     /        |  /    \     /        | /      \   /          |/        \   /          *          \  /          /            \```

The intersecting plane is parallel to the slant of the cone.
The resulting conic curve would be a parabola.

For the plane to pass through the cone,
. . the vertex angle must be less than 82°.