Home
Class 12
MATHS
A hyperbola with eccentricity e=2 has a ...

A hyperbola with eccentricity `e=2` has a focus at (0,0) and corresponding directrix `y-1=0`. The equation of the hyperbola is

A

`x^(2)-3 y^(2)+8 y-4=0`

B

`x^(2)+3 y^(2)+8 y-4=0`

C

`3 x^(2)-y^(2)+8 y-4=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|172 Videos
  • INDEFINITE INTEGRAL

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|404 Videos

Similar Questions

Explore conceptually related problems

An ellipse with eccentricity e=(1)/(2) has a focus at (0,0) and the corresponding directrix x+6=0 . The equation of the ellipse is

A parabola has its focus at (-4,0) and its directrix is x=4 . Its equation is

The vertex of a parabola is (a,0) and the directrix is x+y=3a the equation of the parabola is

The equation of the hyperbola with eccentricity 3/2 and foci at (pm2,0) is

The vertices of a hyperbola are (2,0),(-2,0) and the foci are (3,0),(-3,0) . The equation of the hyperbola is

The parabola with the directrix x+2 y-1=0 and focus (1,0) is

If the focus of a parabola is (0,-3) and its directrix is y =3 then its equation is

The equation of the parabola with focus (0,3) and the directrix y+3=0 is

The equation of the transverse and conugate axes of a hyperbola are respectively 3x+4y-7=0 and 4x-3y+8=0 and their respective lengths are 4 and 6. Find the equation of the hyperbola.

HIMALAYA PUBLICATION-HYPERBOLA-QUESTION BANK
  1. The eccentricity of the hyperbola 4x^(2)-9y^(2)-8x=32 is

    Text Solution

    |

  2. The distance between the foci is 16 and the eccentricity is sqrt(2). T...

    Text Solution

    |

  3. A hyperbola with eccentricity e=2 has a focus at (0,0) and correspondi...

    Text Solution

    |

  4. The equation of the hyperbola with centre (0,0), distance between the ...

    Text Solution

    |

  5. Tangent to hyperbola 4 x^(2)-5 y^(2)=16 at (3,-2) is

    Text Solution

    |

  6. The line 5 x+12 y=9 touch the hyperbola x^(2)-9 y^(2)=9 at

    Text Solution

    |

  7. The conjugate axis of a hyperbola is 8 and passes through (3,-2) . The...

    Text Solution

    |

  8. The tangents to hyperbola 3 x^(2)-y^(2)=3 which are perpendicular to t...

    Text Solution

    |

  9. The equation to the normal to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1...

    Text Solution

    |

  10. The equation of the normal at theta=(pi)/(6) to the hyperbola 3 x^(2)-...

    Text Solution

    |

  11. The normal to hyperbola 4 y^(2)-5 x^(2)=20 at the point (-4,5) is give...

    Text Solution

    |

  12. The asymptotes of the hyperbola are y pm x sqrt(3)=0 and it passes thr...

    Text Solution

    |

  13. The equation of a hyperbola whose asymtotes are 3xpm5y=0 and vertices ...

    Text Solution

    |

  14. The angle between the asymptotes of the hyperbola 3 x^(2)-y^(2)=3 is

    Text Solution

    |

  15. If theta is the angle between the asymptotes of the hyperbola (x^(2))/...

    Text Solution

    |

  16. The asymptote of the hyperbola 9 x^(2)-25 y^(2)=225 are

    Text Solution

    |

  17. The eccentricity of a hyperbola is (5)/(3) then the eccentricity of it...

    Text Solution

    |

  18. The product of the perpendiculars drawn from the hyperbola (x^(2))/(4)...

    Text Solution

    |

  19. If e is the eccentricity of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)...

    Text Solution

    |

  20. The distance of the P on the parabola y^(2)=4 x from the focus is 26. ...

    Text Solution

    |