Home
Class 12
MATHS
P & Q are the points of contact of the t...

P & Q are the points of contact of the tangents drawn from the point T to the parabola `y^(2) = 4ax`. If PQ be the normal to the parabola at P, prove that TP is bisected by the directrix.

Promotional Banner

Topper's Solved these Questions

  • Parabola

    A DAS GUPTA|Exercise EXERCISE|51 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

  • Product of three or more Vectors

    A DAS GUPTA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

Find the points of contact Q and R of a tangent from the point P(2,3) on the parabola y^(2)=4x

If the chord of contact of tangents from a point P to the parabola y^(2)=4ax touches the parabola x^(2)=4by, then find the locus of P.

the tangent drawn at any point P to the parabola y^(2)=4ax meets the directrix at the point K. Then the angle which KP subtends at the focus is

Tangents are drawn from the point (-1,2) to the parabola y^(2)=4x. These tangents meet the line x=2 at P and Q, then length of PQ is

From a point P, tangents PQ and PR are drawn to the parabola y^(2)=4ax . Prove that centroid lies inside the parabola.

From a point P, tangents PQ and PR are drawn to the parabola y ^(2)=4ax. Prove that centrold lies inside the parabola.

If from a point A,two tangents are drawn to parabola y^(2)=4ax are normal to parabola x^(2)=4by, then

A DAS GUPTA-Parabola-EXERCISE
  1. Prove that the normal chord to a parabola at the point whose ordinate ...

    Text Solution

    |

  2. Show that the area formed by the normals to y^2=4ax at the points t1,t...

    Text Solution

    |

  3. P & Q are the points of contact of the tangents drawn from the point T...

    Text Solution

    |

  4. For what values of 'a' will the tangents drawn to the parabola y^2 = 4...

    Text Solution

    |

  5. Find the centre and radius of the smaller of the two circles that touc...

    Text Solution

    |

  6. Prove that the length of the intercept on the normal at the point P(a ...

    Text Solution

    |

  7. Prove that the locus of the middle pointsof chords of the parabolay^2=...

    Text Solution

    |

  8. Prove that the locus of a point, which moves so that its distance from...

    Text Solution

    |

  9. 5. The locus of point of intersection of two tangents to the parabola ...

    Text Solution

    |

  10. Find the locus of the intersection of normals to the parabolay^2=4axat...

    Text Solution

    |

  11. Find the locus of the point of intersection of those normals to the pa...

    Text Solution

    |

  12. Find the locus of point of intersection of tangent to the parabola y^2...

    Text Solution

    |

  13. Find the locus of the middle points of the chords of the parabola y^2=...

    Text Solution

    |

  14. Show that the locus of points such that two of the three normals drawn...

    Text Solution

    |

  15. Prove that the locus of the point of intersection of the normals at th...

    Text Solution

    |

  16. Find the locus of the middle points of the chords of the parabola y^2=...

    Text Solution

    |

  17. If two tangents to the parabola y^2=4ax from a point P make angles ...

    Text Solution

    |

  18. Locus of the feet of the perpendiculars drawn from vertex of the parab...

    Text Solution

    |

  19. If the focus =(2,3)and directrix is x+y=1 then the equation of the par...

    Text Solution

    |

  20. The line x+y+1=0touches the parabola y^2=kx if k=.

    Text Solution

    |