Wallis's conical edge

In geometry, Wallis's conical edge is a ruled surface given by the parametric equations

${\displaystyle x=v\cos u,\quad y=v\sin u,\quad z=c{\sqrt {a^{2}-b^{2}\cos ^{2}u}}}$

where a, b and c are constants.

Wallis's conical edge is also a kind of right conoid. It is named after the English mathematician John Wallis, who was one of the first to use Cartesian methods to study conic sections.^[1]