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Concept

The

Additionally, every ellipse has two axes of symmetry. One runs through both foci, known as the *transverse axis*, while the other, perpendicular to the first, is called the *conjugate axis*. Depending on their orientation, the corresponding ellipse can be called *horizontal* or *vertical*.

Property | Horizontal Ellipse | Vertical Ellipse |
---|---|---|

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

Transverse Axis | Horizontal | Vertical |

Vertices | $(h±a,k)$ | $(h,k±a)$ |

Foci | $(h±c,k)$ | $(h,k±c)$ |

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

In these equations, $a$ and $b$ represent half the lengths of the major and minor axes, respectively, while $(h,k)$ denotes the center of the ellipse.

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