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{{ printedBook.courseTrack.name }} {{ printedBook.name }} A hyperbola is the set of all points in a plane such that the absolute value of the differences of the distances from the foci is constant.

Any hyperbola has two axes of symmetry: one that passes through both foci, called the *transverse axis,* and another that is perpendicular to the first and equidistant from both curves, called the *conjugate axis*.

The above graph is an example of a horizontal hyperbola. Notice that the transverse axis is a horizontal line. There are also vertical hyperbolas where the transverse axis is a vertical line. Below is a list of the properties of horizontal and vertical 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.