Home
Class 12
MATHS
The normals are drawn from (2lamda,0) to...

The normals are drawn from `(2lamda,0)` to the parabola `y^2=4x` .Show that `lamda` must be greater than 1. One normal is always the X-axis. Find `lamda` for which the other two normals are perpendicular to each other.

Text Solution

Verified by Experts

The correct Answer is:
`lamda=3/2`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise For Session 1|20 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

Similar Questions

Explore conceptually related problems

Three normals are drawn from the point (c,0) to the curve y^2=x . Show that c must be greater than (1)/(2) . One normal is always the X-axis. Find c for which the other two normals are perpendicular to each other.

Three normals are drawn from the point (c,0) to the curve y^2=x . Show that c must be greater than 1/2 . One normal is always the x-axis. For what values of c are the other two normals perpendicular to each other

The number of normals drawn to the parabola y^(2)=4x from the point (1,0) is

Three normals are drawn from the point (c,0) to the parabola y^(2)=x ,One normal is the x-axis .If the other two normal are perpendicular to each other.Then value of c is (a)/(b) where a and b are relative prime then a+b=

Three normals are drawn from the point (a,0) to the parabola y^2=x . One normal is the X-axis . If other two normals are perpendicular to each other , then the value of 4a is

Three normals are drawn from (k,0) to the parabola y^(2)=8x one of the normal is the axis and the remaining normals are perpendicular to each other,then find the value of k.

Three normals are drawn to the parabola y^(2) = 4x from the point (c,0). These normals are real and distinct when

The number of distinct normals that be drawn from (-2,1) to the parabola y^(2)-4x-2y-3=0 is:

ARIHANT MATHS-PARABOLA-Exercise For Session 2
  1. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

    Text Solution

    |

  2. The set of points on the axis of the parabola y^2-4x-2y+5=0 from which...

    Text Solution

    |

  3. Prove that any three tangents to a parabola whose slopes are in harmon...

    Text Solution

    |

  4. prove that the locus of the point of intersection of the tangents at t...

    Text Solution

    |

  5. Find the equation of the normal to the parabola y^2=4x which is para...

    Text Solution

    |

  6. Find the equation of the normal to the parabola y^2=4x which is perp...

    Text Solution

    |

  7. The ordinates of points P and Q on the parabola y^2=12x are in the rat...

    Text Solution

    |

  8. The normals at P, Q, R on the parabola y^2 = 4ax meet in a point on th...

    Text Solution

    |

  9. The normals are drawn from (2lamda,0) to the parabola y^2=4x .Show tha...

    Text Solution

    |

  10. If m1,m2 are the slopes of the two tangents that are drawn from (2,3) ...

    Text Solution

    |

  11. The angle between the tangents drawn from the origin to the parabola y...

    Text Solution

    |

  12. IF (a,b) is the mid point of chord passing through the vertex of the p...

    Text Solution

    |

  13. The diameter of the parabola y^2=6x corresponding to the system of par...

    Text Solution

    |

  14. Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The ...

    Text Solution

    |

  15. for parabola x^2+y^2+2xy−6x−2y+3=0, the focus is (a) (1,-1) (b) (-1,1...

    Text Solution

    |

  16. Find the locus of the mid-points of the chords of the parabola y^2=4ax...

    Text Solution

    |

  17. A ray of light moving parallel to the X-axis gets reflected from a par...

    Text Solution

    |

  18. The locus of the point of intersection of the tangents to the parabola...

    Text Solution

    |

  19. The lacus of the middle points of the chords of the parabola y^(2)=4ax...

    Text Solution

    |

  20. Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The ...

    Text Solution

    |