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

[pcm]

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.

 

[Jorriss]

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.

 

[pcm]

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

 

[oli4]

Hi pcm,
maybe this link will be helpful ?
Cheers...

 

[pcm]

thanks Jorriss and oli4 for your help.