Equation of an Upward Facing Cone

[laz0r]

I'm having a little bit of trouble understanding the equation of a cone..

It is given by (x^2)/(a^2) + (y^2)/(b^2) = (z^2)/(c^2)

I understand that if a ≠ b you have an elliptical cone, but I'm not sure how to set the equation up to define the cone as having a height.

Can anyone clarify how to do this?

 

[gopher_p]

I'd suggest that you examine the graph of the equation $\frac{x^2}{a^2}=\frac{y^2}{b^2}$, the 2-D analogue of the equation that you're interested in. It might give you insight into (a) what the graph of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=\frac{z^2}{c^2}$ really looks like (it's not just an upward-facing cone) and (b) what you might need to do in order to force it to be (i) an upward-facing cone with (ii) a finite height.