In geometry, a **right conoid** is a ruled surface generated by a family of straight lines that all intersect perpendicularly to a fixed straight line, called the *axis* of the right conoid.

Using a Cartesian coordinate system in three-dimensional space, if we take the z-axis to be the axis of a right conoid, then the right conoid can be represented by the parametric equations:

where *h*(*u*) is some function for representing the *height* of the moving line.

## Examples

A typical example of right conoids is given by the parametric equations

The image on the right shows how the coplanar lines generate the right conoid.

Other right conoids include:

- Helicoid:
- Whitney umbrella:
- Wallis's conical edge:
- Plücker's conoid:
- hyperbolic paraboloid: (with x-axis and y-axis as its axes).

## See also

## External links

- "Conoid",
*Encyclopedia of Mathematics*, EMS Press, 2001 [1994] - Right Conoid from MathWorld.
- Plücker's conoid from MathWorld