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## Euclidean Normal Forms of Two-Dimensional Quadrics |

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z | overview |

There exist appropriate Cartesian coordinate systems with respect to which the equations defining quadrics have the following normal forms.

**conical quadrics**

normal form | name |

point | |

intersecting pair of lines | |

coincident lines |

**central quadrics**

normal form | name |

(empty set) | |

hyperbola | |

ellipse | |

(empty set) | |

parallel pair of lines |

**parabolic quadrics**

normal form | name |

parabola |

The normal forms are uniquely determined up to permutation of subscripts and in the case of conical quadrics up to multiplication by a constant .

The values are set to be positive and are called lengths of the principal axes of the quadric.

intersecting pair of lines | coincident lines |

hyperbola | ellipse |

parallel pair of lines | parabola |

automatically generated 7/13/2018 |