What is the shape of the surface defined by a(x²+y²)+bz²=c?

  • Context: Undergrad 
  • Thread starter Thread starter pcm
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Discussion Overview

The discussion revolves around the shape of the surface defined by the equation a(x²+y²)+bz²=c, exploring how different values of the parameters a, b, and c affect the surface's geometry. Participants are interested in understanding the implications of these parameters in the context of a physics problem.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks about the shape of the surface for various positive and negative values of a, b, and c.
  • Another suggests rearranging the equation to a'(x²+y²) = c' - z² and proposes examining specific values of z to gain insight into the shape.
  • A participant notes that for positive values of a', b', and c', as one moves up the z-axis, the radius of the circle decreases, prompting a question about the overall shape.
  • One participant shares a link that may provide additional helpful information.
  • A participant expresses gratitude for the assistance received from others in the discussion.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the shape of the surface, and multiple viewpoints regarding the effects of different parameter values remain present.

Contextual Notes

Participants have not fully resolved the implications of the parameters a, b, and c on the surface shape, and there are assumptions about the conditions under which the surface is analyzed.

pcm
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a(x2+y2)+bz2=c

what is the shape of the surface for different values(+ve, -ve) of a,b,c.
i wanted to know in which class i will come across these things.
i found this while solving a physics problem and i have no idea about the shape of given surface.
 
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Perhaps it would help to rearrange it a bit.

a'(x^2+y^2) = c' -z^2

And then, maybe to start, see what it looks like for z=0, 1 and, say, 2.
 
Last edited:
ok so for positive a',b',c'
as i go up the z axis the radius of the circle goes on decreasing.
so what is the shape?
same idea should work for other signs of a,b,c
 
Last edited:
Hi pcm,
maybe this link will be helpful ?
Cheers...
 
thanks Jorriss and oli4 for your help.
 

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