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Subject: "CONICS"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #588
Reading Topic #588
Venkat Ramayya
guest
Oct-02-06, 04:07 PM (EST)
 
"CONICS"
 
   I have a doubt.

Is it possible to get rectangular hyperbola when we cut a cone with a section plane parallel to axis of the cone with any dimensions?


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alexbadmin
Charter Member
1893 posts
Oct-02-06, 10:44 PM (EST)
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1. "RE: CONICS"
In response to message #0
 
   >Is it possible to get rectangular hyperbola when we cut a
>cone with a section plane parallel to axis of the cone with
>any dimensions?

I am not sure about the meaning of "with any dimensions". Do you mean to ask whether any cone can be cut to produce a rectangular hyperbola? The answer to that question would be No. You should just consider a needle like cone. A rectangular hyperbola needs some room.


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Maj. Pestich
guest
Oct-03-06, 12:38 PM (EST)
 
2. "RE: CONICS"
In response to message #1
 
   This is correct.

We even have a special guarded room with controlled

temperature and pressure where on the shelves

a set of cones is kept, including cones for

parabolas and ellipses, just like diffrent

sets of auto wrenches in a body shop.

Maj. Pestich.


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Venkat Ramayya
guest
Oct-04-06, 08:22 AM (EST)
 
3. "RE: CONICS"
In response to message #1
 
   I saw the answer by you.

Let me put it like this.

We ger a Rect hyperbola when we cut a cone with a section
plnne parallel to the axis, whose height is equal to the base radius.

Now is it possible to get Rect. Hyperbola for cones with other dimensions?


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alexbadmin
Charter Member
1893 posts
Oct-04-06, 08:48 AM (EST)
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4. "RE: CONICS"
In response to message #3
 
   >Now is it possible to get Rect. Hyperbola for cones with
>other dimensions?

I imagine Yes.

Wobble the cross plane in a direction to the axis of the cone. You'll get hyperbolic cross sections. Without any calculations, I'd think that the angle between the asymptotes changes, even if a little. (This must be true because eventually you'd get a parabola.) Thus you must be able to get a rectangular hyperbola by choosing a proper cone apex angle and the angle of inclination of the cone to the cross plane.


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