Equations
A conical surface can be described parametrically as
- ,
where is the apex and is the directrix.
A right circular conical surface of aperture, whose axis is the coordinate axis, and whose apex is the origin, it is described parametrically as
where and range over and, respectively. In implicit form, the same surface is described by where
More generally, a right circular conical surface with apex at the origin, axis parallel to the vector, and aperture, is given by the implicit vector equation where
or
where, and denotes the dot product.
In three coordinates, x, y and z, the general equation for a cone with apex at origin is a homogenous equation of degree 2 given by
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