# Right conoid

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

- Hazewinkel, Michiel, ed. (2001), "Conoid",
*Encyclopedia of Mathematics*, Springer, ISBN 978-1-55608-010-4 - Right Conoid from MathWorld.
- Plücker's conoid from MathWorld

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