Home
Class 12
MATHS
Find the eccentricity and length of the ...

Find the eccentricity and length of the latus rectum of the hyperbola
(i) `4x^(2) - 9y^(2) = 27`
(ii) `x^(2) - 9y^(2) = 27`

Text Solution

Verified by Experts

The correct Answer is:
(i) `(4)/(sqrt(3))`
(ii) `(2)/(sqrt(3))`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    AAKASH SERIES|Exercise Exercise|6 Videos
  • HYPERBOLA

    AAKASH SERIES|Exercise Examples|10 Videos
  • EXPONENTIAL SERIES

    AAKASH SERIES|Exercise EXERCISE - III|8 Videos
  • INDEFINITE INTEGRALS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|167 Videos

Similar Questions

Explore conceptually related problems

The length of the latus rectum of the hyperbola x^(2) -4y^(2) =4 is

The length of the latus rectum of the hyperbola 25x^(2)-16y^(2)=400 is

Find the corrdinates of the foci and the vertices, the eccentricity, the length of the latus rectum of the hyperbolas : (i) (x^(2))/(9)-(y^(2))/(16)=1 (ii) y^(2)-16x^(2)=16

The length of the latus rectum of the hyperbola 9x^(2) -16y^(2) +72x -32y- 16 =0 is

The length of the latus rectum of the parabola 3x^(2)-9x+5y-2=0 is

The length of the latus rectum of the parabola y^(2)+8x-4y-4=0 .

The length of the latus rectum of the parabola x^(2)-4x+8y+28=0 is

Find the centre, eccentricity, foci directrices and the length of the latus rectum of the following hyperbolas (i) 4x^(2) - 9y^(2) - 8x - 32 = 0 (ii) 4(y + 3)^(2) + 9(x - 2)^(2) = 1

AAKASH SERIES-HYPERBOLA-Solved Examples
  1. Find the eccentricity, foci, length of latusrectum and the equations t...

    Text Solution

    |

  2. The equation of the hyperbola whose focus is origin, eccentricity sqr...

    Text Solution

    |

  3. Find the eccentricity and length of the latus rectum of the hyperbola ...

    Text Solution

    |

  4. Find the foci of the hyperbola 9x^(2) - 16y^(2) + 72 x - 32 y - 16 = 0

    Text Solution

    |

  5. Find the eccentricity foci, equation of the directrices and length of ...

    Text Solution

    |

  6. (i) Show that equation (x^(2))/(9 - c) + (y^(2))/(5 - c) = 1 represent...

    Text Solution

    |

  7. The foci of a hyperola coincide with the foci of the ellipse x^(2)/(25...

    Text Solution

    |

  8. Find the equations of the tangents to the hyperbola x^(2) - 4y^(2) = 4...

    Text Solution

    |

  9. Tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angle...

    Text Solution

    |

  10. The equations of the tangents to the hyperbola 3x^(2) -4y^(2) =12 whi...

    Text Solution

    |

  11. Find the equation of the normal at (1, 0) on the hyperbola x^(2) - 4y...

    Text Solution

    |

  12. Tangents are drawn from (0, 2) to the hyperbola 5x^(2) - y^(2) = 5 . ...

    Text Solution

    |

  13. The chord of the hyperbola x^(2)/a^(2)-y^(2)/b^(2)=1, whose equation i...

    Text Solution

    |

  14. Find the condition for the line x cos alpha + y sin alpha = p to be t...

    Text Solution

    |

  15. Prove that the product of the lengths of the perpendicular drawn from ...

    Text Solution

    |

  16. The point of intersection of the asymptotes with the directrices lie o...

    Text Solution

    |

  17. Write down the equation of the normal at theta = (pi)/(3) to the hyper...

    Text Solution

    |

  18. Prove that the product of the perpendicular from any point on the hype...

    Text Solution

    |

  19. If the normal at theta on the hyperola x^(2)/a^(2)-y^(2)/b^(2)=1 meets...

    Text Solution

    |

  20. If a circle cuts the rectangular hyperbola xy = 1 in the points (x(r),...

    Text Solution

    |