Essentially, this boils down to finding the equation of an ellipse formed by slicing a cone at a random angle. Now let me explain more: I have an equation for a cone which is at a specific angle (say 54 degrees above the x-y plane). I want to find the ellipse formed from it onto the x-y plane. I have the equation of the circle sliced perpendicular to the cone axis at the specific point, however, I don't know where to go from there. How can I find the projection of this circle onto the x-y plane?
I'm not sure if I'm right, but shouldn't this ellipse have a longer major axis than the original circle's diameter?
Although I saw a similar thread, it wasn't super helpful, for I ran into some problems with it. The circle became an ellipse, but the major axis stayed the same as the circle's original diameter.
Thanks for any help!
Edit: I started with a cone whose equation was:
$\frac{1}{217.5^2}(z+6.802)^2=x^2+y^2$
I then changed this into a vector function:
$<x\space,\space y\space,\space217.5\sqrt{x^2+y^2}-6.802>$
Next, I rotated the cone 54° up about $x=0$ and 214.5° around $z'=0$.
As you can imagine, this vector became ugly as sin.