= Elliptic cone
{title2=$a u^2=b v^2+c w^2,\quad a,b,c>0$}
An elliptic cone is a real <quadric surface> consisting of the two nappes $u=\pm\sqrt{(bv^2+cw^2)/a}$, joined at the vertex. Its intersections with planes $u=u_0\ne0$ are <ellipses>. It is the zero level of an indefinite <quadratic form> of <signature> $(1,2)$. Changing the level to a positive value produces a <two-sheeted hyperboloid>; changing it to a negative value produces a <one-sheet hyperboloid>, when the positive coefficient is assigned to the axial coordinate $u$.
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