Home
Class 12
MATHS
Find the equations of the tangents to th...

Find the equations of the tangents to the hyperbola `x^(2) - 4y^(2) = 4` which are
(i) parallel and , (ii) perpendicular to the line x + 2y = 0

Text Solution

Verified by Experts

The correct Answer is:
(i) `rArr x + 2y = 0`
(ii) `2x - y pm sqrt(15) = 0`
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

Find the equations of the tangents to the hyperbola 3x^(2) - 4y^(2) = 12 which are (i) parallel and (ii) perpendicular to the line y = x - 7

Find the equation of the tangents to the hyperbola 3x^(2)-4y^(2)=12 which are (i) Parallel and (ii) perpendicular to the line y=x-7

Find the equation of tangent to the hyperbola 3x^(2) - 4y^(2) = 8 at (2, - 1)

Find the equation of tangents to, the hyperbola x^2-4y^2 = 4 which are parallel x+2y=0.

Find the equations of the tangents to the ellipse 2x^(2) + y^(2) = 8 which are (i) parallel to x - 2y - 4 (ii) perpendicular to x + y + 2 = 0

Find the equation of the tangent to the hyperbola 4x^(2)-9y^(2)=36" at "theta=pi/4

Find the equation of the tangents to the hyperbola x^(2)-4y^(2)=4 which are parallel and perpendicular to the line x+2y=0

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

Find the equation of the tangents to the hyperbola x^(2)-4y^(2)=4 which are Perpendicular to the line x+2y=0

The equation of the tangents to the hyperbola 3x^(2) -4y^(2) =12 which are parallel to the line 2x+ y+7=0 are

AAKASH SERIES-HYPERBOLA-Solved Examples
  1. (i) Show that equation (x^(2))/(9 - c) + (y^(2))/(5 - c) = 1 represent...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Find the equation of the chord joining two points (x(1), y(1))and (x(2...

    Text Solution

    |

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

    Text Solution

    |

  18. Find the centre, eccentricity, foci directrices and the length of the ...

    Text Solution

    |

  19. Find the equations of the tangents to the hyperbola 3x^(2) - 4y^(2) = ...

    Text Solution

    |

  20. Prove that the point of intersection of two perpendicular tangents tot...

    Text Solution

    |