A cone is the union of a set of half-lines that start at a common apex point and go through a base which can be any parametric curve. Show that the graph of z = ( x ^2 + 4y ^2)^(1/2) is a cone. What can be chosen as its base? Sketch the base.
I can see how I show this is cone by hand, just squaring and dividing across by 4 to get (z^2)/4=(x^2)/4 + y^2 but not sure how I can sketch it mathematica, including the base. Do I have to change it from this form? Is it Plot 3-D or is it parametric plot as I'll need to use something as a base. Anyone got any advice?