Given the hyperbola below

calculate the equation of the asymptotes

intercepts, foci points

eccentricity and other items.

y^{2} | |

100 |

- |

x^{2} | |

49 |

= |

1 |

Since our first variable is y

the hyperbola has a *vertical* transverse axis

a = √100

a = 10

b = √49

b = 7

Asymptote 1 = | ax |

b |

Asymptote 1 = | 10x |

7 |

Asymptote 2 = | -ax |

b |

Asymptote 2 = | -10x |

7 |

y-intercepts = ±a

y-intercepts = ±10

y-intercepts =(0, 10) and (0, -10)

Our foci are at (0,c) and (0,-c) where

a^{2} + b^{2} = c^{2}

Therefore, c = √a^{2} + b^{2}

a = √10^{2} + 7^{2}

c = √100 + 49

c = √149

c = 12.206555615734

Foci = (0,12.206555615734) and (0,-12.206555615734)

ε = | c |

a |

ε = | 12.206555615734 |

10 |

ε = 1.2206555615734

Latus Rectum = | 2b^{2} |

a |

Latus Rectum = | 2(7)^{2} |

10 |

Latus Rectum = | 2(49) |

10 |

Latus Rectum = | 98 |

10 |

Latus Rectum = 9.8

l = | Latus Rectum |

2 |

l = | 9.8 |

2 |

l = 4.9

hyperbola has a *vertical*

y-intercepts =**(0, 10) and (0, -10)**

Foci = (0,12.206555615734) and (0,-12.206555615734)

ε = 1.2206555615734

Latus Rectum =**9.8**

l =**4.9**

y-intercepts =

Foci = (0,12.206555615734) and (0,-12.206555615734)

ε = 1.2206555615734

Latus Rectum =

l =

hyperbola has a *vertical*

y-intercepts =**(0, 10) and (0, -10)**

Foci = (0,12.206555615734) and (0,-12.206555615734)

ε = 1.2206555615734

Latus Rectum =**9.8**

l =**4.9**

y-intercepts =

Foci = (0,12.206555615734) and (0,-12.206555615734)

ε = 1.2206555615734

Latus Rectum =

l =

Free Hyperbola Calculator - Given a hyperbola equation, this calculates:

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

This calculator has 1 input.

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

This calculator has 1 input.

standard form of a hyperbola that opens sideways is (x - h)^{2} / a^{2} - (y - k)^{2} / b^{2} = 1

standard form of a hyperbola that opens up and down, it is (y - k)^{2} / a^{2} - (x - h)^{2} / b^{2} = 1

For more math formulas, check out our Formula Dossier

standard form of a hyperbola that opens up and down, it is (y - k)

For more math formulas, check out our Formula Dossier

- asymptote
- a line that continually approaches a given curve but does not meet it at any finite distance
- foci
- special points with reference to which any of a variety of curves is constructed
- hyperbola
- conic section defined as the locus of all points in the plane the difference of whose distances and from two fixed points
- intercept

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