Home
Class 11
MATHS
The lengths of transverse and conjugate ...

The lengths of transverse and conjugate axes of a hyperbola are 4 unit and 6 unit respectively and their equations are x + 3 = 0 and y - 1 = 0, find the equation of the hyperbola.

Text Solution

Verified by Experts

The correct Answer is:
`9x^(2)-4y^(2)+ 54x + 8y + 41 = 0`
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise LONG ANSWER TYPE|10 Videos

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMS|12 Videos

  • HYPERBOLA

    CHHAYA PUBLICATION|Exercise VERY SHORT ANSWER TYPE QUESTIONS|1 Videos

  • DIAGRAMMATIC REPRESENTATION OF DATA

    CHHAYA PUBLICATION|Exercise EXERCISE (Very short Answer Type Question)|7 Videos

  • MATHEMATICAL INDUCTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams|20 Videos

Similar Questions

Explore conceptually related problems

The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y-3=0 and 2x-y+4=0 , and their respective lengths are sqrt(2) and 2/sqrt(3)dot The equation of the hyperbola is a) 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 b) 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 c) 2/5(2x-y+4)^2-3/5(x+2y-3)^2=1 d) 2(x+2y-3)^2-3(2x-y+4)^2=1

The lengths of major and minor axes of an ellipse are 8 and 6 and their equations are y - 1 = 0 and x + 3 = 0 respectively . Find the equation of the ellipse .

Find the length of the transverse and conjugate axes of the hyperbola 9x^(2) - 16y^(2) = 144 . Write down the equation of the hyperbola conjugate to it and find the eccentricities of both the hyperbolas.

If the centre, vertex and focus of a hyperbola be (0,0), (4,0) and (6,0) respectively, then the equation of the hyperbola is

The equation of the axis and directrix of a parabola are y - 3 = 0 and x + 3 = 0 respectively and the length of the latus rectum is 8 units . Find the equation of the parabola and the coordinate of its vertex .

The equation of the axis and directrix of a parabola are y-3=0 and x+3=0 respectively and the length of the latus tectum is 8 units.find the equation of the parabola and the coordinates of its verex.

If normal at P to a hyperbola of eccentricity e intersects its transverse and conjugate axes at L and M, respectively, then prove that the locus of midpoint of LM is a hyperbola. Find the eccentricity of this hyperbola

If the length of latus rectum of a rectangular hyperbola is 6 unit, find its equation.

Find the equation of the ellipse whose axes are of length 6 and 2sqrt(6) and their equations are x-3y+3=0 and 3x+y-1=0 , respectively.

The length of the transverse axis of the hyperbola 9x^(2)-16y^(2)-18x -32y - 151 = 0 is

CHHAYA PUBLICATION-HYPERBOLA-SHORT ANSWER TYPE QUESTIONS
  1. The hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1 passes through the p...

    Text Solution

    |

  2. Find the equation of the hyperbola whose eccentricity is(5)/(4), foc...

    Text Solution

    |

  3. Find the equation of the hyperbola whose eccentricity is (5)/(4), f...

    Text Solution

    |

  4. Find the equation of the hyperbola whose eccentricity is sqrt(3), fo...

    Text Solution

    |

  5. Find the equation of the hyperbola whose eccentricity is sqrt(2), fo...

    Text Solution

    |

  6. Find the equation of the hyperbola whose eccentricity is sqrt(2), fo...

    Text Solution

    |

  7. Find the equation of the hyperbola whose eccentricity is 3, focus is...

    Text Solution

    |

  8. Find the equation of the hyperbola, referred to its axes as lines para...

    Text Solution

    |

  9. The distance between the vertices of a hyperbola is half the distance ...

    Text Solution

    |

  10. The coordinates of the foci of a hyperbola are (16,0) and (-8,0) and i...

    Text Solution

    |

  11. The centre of a hyperbola is at (2,4), the coordinates of one of its v...

    Text Solution

    |

  12. Find the equation of the hyperbola centre at the origin, transeverse a...

    Text Solution

    |

  13. The lengths of transverse and conjugate axes of a hyperbola are 4 unit...

    Text Solution

    |

  14. e(1) and e(2) are respectively the eccentricites of a hyperbola and it...

    Text Solution

    |

  15. Find the eccentricity of the hyperbola x^(2) - y^(2) = 1. If S, S(1) a...

    Text Solution

    |

  16. P is a veriable poin on the hyperbola x^(2) - y^(2) =16 and A (8,0) is...

    Text Solution

    |

  17. Show that the difference of focal distances of any point of the hyperb...

    Text Solution

    |

  18. The coordinates of the foci of a hyperbola are (0,4) and (0,-4) and th...

    Text Solution

    |

  19. Show that for all values of t the point x = a. (1 + t^(2))/(1-t^(2)), ...

    Text Solution

    |

  20. Show that x =3(cotmu + tanmu), y =4(cotmu - tanmu) where mu is a veria...

    Text Solution

    |