Exploring the Surface Equation a(x2+y2)+bz2=c in Physics Problems

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In summary, the conversation is about the shape of a surface represented by the equation a(x2+y2)+bz2=c. The participants discuss different values of a, b, and c and how they affect the shape of the surface. They also mention rearranging the equation and trying different values for z to better understand the shape. One participant suggests using a link for further help.
  • #1
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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  • #2
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:
  • #3
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:
  • #4
Hi pcm,
maybe this link will be helpful ?
Cheers...
 
  • #5
thanks Jorriss and oli4 for your help.
 

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