There are 17 standard-form quadratic surfaces. The general quadratic is written

(1) |

(2) | |||

(3) | |||

(4) | |||

(5) | |||

(6) |

and , , as are the roots of

(7) |

(8) |

Surface | Equation | ||||

Coincident Planes | 1 | 1 | |||

Ellipsoid (Imaginary) | 3 | 4 | 1 | ||

Ellipsoid (Real) | 3 | 4 | 1 | ||

Elliptic Cone (Imaginary) | 3 | 3 | 1 | ||

Elliptic Cone (Real) | 3 | 3 | 0 | ||

Elliptic Cylinder (Imaginary) | 2 | 3 | 1 | ||

Elliptic Cylinder (Real) | 2 | 3 | 1 | ||

Elliptic Paraboloid | 2 | 4 | 1 | ||

Hyperbolic Cylinder | 2 | 3 | 0 | ||

Hyperbolic Paraboloid | 2 | 4 | 0 | ||

Hyperboloid of one Sheet | 3 | 4 | 0 | ||

Hyperboloid of two Sheets | 3 | 4 | 0 | ||

Intersecting Planes (Imaginary) | 2 | 2 | 1 | ||

Intersecting Planes (Real) | 2 | 2 | 0 | ||

Parabolic Cylinder | 1 | 3 | |||

Parallel Planes (Imaginary) | 1 | 2 | |||

Parallel Planes (Real) | 1 | 2 |

**References**

Beyer, W. H. *CRC Standard Mathematical Tables, 28th ed.* Boca Raton, FL: CRC Press, pp. 210-211, 1987.

© 1996-9

1999-05-25