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Concept

Every hyperbola has two axes of symmetry. One runs through both foci, known as the transverse axis, while the other, perpendicular to the first, is equidistant from both curves, called the conjugate axis. For this hyperbola the transverse axis and conjugate axis are the $x-$axis and $y-$axis, respectively.

In this graph the transverse axis runs horizontally. There are also vertical hyperbolas, where the transverse axis is vertical. Below you can find the properties of both types of hyperbolas.

Property | Horizontal Hyperbola | Vertical Hyperbola |
---|---|---|

General Equation | $a_{2}(x−h)_{2} −b_{2}(y−k)_{2} =1$ | $a_{2}(y−k)_{2} −b_{2}(x−h)_{2} =1$ |

Transverse Axis | Horizontal | Vertical |

Vertices | $(h±a,k)$ | $(h,k±a)$ |

Foci | $(h±c,k)$ | $(h,k±c)$ |

Asymptotes | $y−k=±ab (x−h)$ | $y−k=±ab (x−h)$ |

$c-value$ | $c_{2}=a_{2}+b_{2}$ | $c_{2}=a_{2}+b_{2}$ |

Although these curves are not considered to be parabolas, they do have foci and directrices as parabolas do.

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