Home
Class 12
MATHS
The equation of the hyperbola in the sta...

The equation of the hyperbola in the standard form (with transverse axis along the `x` -axis) having the length of the latus rectum `=9` units and eccentricity `=(5)/(4)` is

A

`(x^(2))/(16)-(y^(2))/(18)=1`

B

`(x^(2))/(36)-(y^(3))/(27) .=1`

C

`(x^(2))/(64)-(y^(2))/(36)=1`

D

`(x^(2))/(36)-(y^(2))/(64)=1`

Text Solution

Verified by Experts

The correct Answer is:
C
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

The length of the latus rectum of 3x^(2)-4y+6x-3=0 is

Find the equation of hyperbola in the standard form given that length of L.R. =(14)/(3)&e=(4)/(3) .

Find the equations of the hyperbola satisfying the given conditions. Foci (+-5,0) , the transverse axis is of length 8 .

If the parabola y^(2)=4 a x passes through (3,2) then the length of the latus rectum is

If the parabola x^(2)=4xy passes through the point (2, 1) , then the length of the latus rectum is

Find the equation of the hyperbola where foci are (0,+-12) and the length of the latus rectum is 36 .

Find the coordinates of the vertices, length of the latus rectum and eccentricity of the ellipse x^(2)/49 + y^(2)/36 = 1

Find the equation of the ellipse, with major axis along the x-axis and passing through the points (4,3) and (-1,4)

The length of the latus rectum of the ellipse 25x^(2) + 4y^(2) = 100 , is

HIMALAYA PUBLICATION-HYPERBOLA-QUESTION BANK
  1. If the eceentricity of a hyperbola is sqrt(7) then the eccentricity of...

    Text Solution

    |

  2. Any point on the hyperbola ((x+1)^(2))/(16)-((y-2)^(2))/(4)=1 is of ...

    Text Solution

    |

  3. The equation of the hyperbola in the standard form (with transverse ax...

    Text Solution

    |

  4. The line x+y=sqrt(2) p will touch the hyperbola 4 x^(2)-9 y^(2)=36, if

    Text Solution

    |

  5. The difference of focal distance of any point on the hyperbola (x^(2))...

    Text Solution

    |

  6. The tangents from a point (2 sqrt(2), 1) to the hyperbola 16 x^(2)-25 ...

    Text Solution

    |

  7. The locus of the point of intersection of perpendicular tangents to th...

    Text Solution

    |

  8. The angle between the two asymptotes of the hyperbola (x^(2))/(16)-(y^...

    Text Solution

    |

  9. The product of the perpendicular from any poitn P(x,y) on the hyperbol...

    Text Solution

    |

  10. The equation of the hyperbol whose foci are (-2,0) and (2,0) and eccen...

    Text Solution

    |

  11. The asymptotes of a hyperbola are the coordinate axes. If the hyperbol...

    Text Solution

    |

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

    Text Solution

    |

  13. The eccentricity of the hyperbola with asymptotes 3 x+4 y=2 and 4 x-3 ...

    Text Solution

    |

  14. The equation of a tangent parallel to y=x drawn to (x^(2))/(3)-(y^(2))...

    Text Solution

    |

  15. The eccentricity of the hyperbola 9 x^(2)-16 y^(2)-18 x-64 y-199=0 i...

    Text Solution

    |

  16. Let P(a sec theta,b tan theta) and Q(a sec varphi, b tan varphi) where...

    Text Solution

    |

  17. The equation (x^(2))/(1-r)+(y^(2))/(r-3)+1=0 represents an ellipse if ...

    Text Solution

    |

  18. If the line y=3 x+lambda touches the hyperbola 9 x^(2)-5 y^(2)=45, the...

    Text Solution

    |

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

    Text Solution

    |

  20. If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in f...

    Text Solution

    |