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Equation of an Upward Facing Cone

  1. Apr 4, 2014 #1
    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?
  2. jcsd
  3. Apr 4, 2014 #2
    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.
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