# Standard Equations of Ellipse

**Equation of ellipse:**

*a***>**

**b**Center | (0, 0) |

Vertices | (Â±a, 0) |

Length of major axis | 2a |

Length of minor axis | 2b |

Foci | (Â± ae, 0) |

Equation of directrices | x = Â± a/e |

Relation in a, b, and e |
b^{2} = a^{2} (1 â€“ e^{2}) |

Length of the rectum | |

Ends of latus rectum | |

Equation of auxiliary circle (circle described on major axis as diameter) |
x^{2} + y^{2} = a^{2}, Q has coordinates (a cos Ï†, a sin Ï†) P is corresponding point on the ellipse which has coordinates (a cos Ï†, b sin Ï†) |

Focal radii of any point P(x_{1}, y_{1}) on ellipse |
SP = a â€“ ex_{1} and Sâ€²P = a + ex_{1} |

Sum of focal radii SP + Sâ€²P |
2a |

*b*> aCenter | (0, 0) |

Vertices | (0, Â± b) |

Length of major axis | 2b |

Length of minor axis | 2a |

Foci | (0, Â± be) |

Equation of directrices | y = Â± b/e |

Relation in a, b, and e |
a^{2} = b^{2} (1 â€“ e^{2}) |

Length of the rectum | |

Ends of latus rectum | |

Equation of auxiliary circle (circle described on major axis as diameter) |
x^{2} + y^{2}= b^{2}, Q has coordinates (b cos Ï†, b sin Ï†) P is corresponding point on the ellipse which has coordinates (a cos Ï†, b sin Ï†) |

Focal radii of any point P(x_{1}, y_{1}) on ellipse |
SP = b â€“ ey_{1} and Sâ€²P =b + ey_{1} |

Sum of focal radii SP + Sâ€²P |
2b |