Home
Class 12
MATHS
If the normals at two points P and Q of ...

If the normals at two points P and Q of a parabola `y^2 = 4ax` intersect at a third point R on the curve, then the product of ordinates of P and Q is (A) `4a^2` (B) `2a^2` (C) `-4a^2` (D) `8a^2`

A

`4 a^2`

B

`2a^2`

C

`-4a^2`

D

`8a^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • THE PARABOLA

    ML KHANNA|Exercise Problem Set (3) (TRUE AND FALSE)|4 Videos

  • THE PARABOLA

    ML KHANNA|Exercise Problem Set (3) (FILL IN THE BLANKS)|5 Videos

  • THE PARABOLA

    ML KHANNA|Exercise Problem Set (2) (FILL IN THE BLANKS)|5 Videos

  • THE HYPERBOLA

    ML KHANNA|Exercise SELF ASSESSMENT TEST |4 Videos

  • THEORY OF QUADRATIC EQUATIONS

    ML KHANNA|Exercise Self Assessment Test|27 Videos

Similar Questions

Explore conceptually related problems

If the normals at two points P and Q of a parabola y^2 = 4x intersect at a third point R on the parabola y^2 = 4x , then the product of the ordinates of P and Q is equal to

If the tangents at the points P and Q on the parabola y^2 = 4ax meet at R and S is its focus, prove that SR^2 = SP.SQ .

If tangent at P and Q to the parabola y^(2)=4ax intersect at R then prove that mid point the parabola,where M is the mid point of P and Q.

Normals at points P, Q and R of the parabola y^(2)=4ax meet in a point. Find the equation of line on which centroid of the triangle PQR lies.

If the normal at points (p_(1),q_(1)) and (p_(2),q_(2)) on the parabola y^(2)=4ax intersect at the parabola,then the value of q_(1).q_(2) is

Normals are drawn at points P, Q are R lying on the parabola y^(2)=4x which intersect at (3, 0), then

The tangent and normal at the point P(4,4) to the parabola, y^(2) = 4x intersect the x-axis at the points Q and R, respectively. Then the circumcentre of the DeltaPQR is

ML KHANNA-THE PARABOLA -Problem Set (3) (MULTIPLE CHOICE QUESTIONS)
  1. If the normals at points 't1' and 't2' meet on the parabola, then

    Text Solution

    |

  2. The equation of a normal to the parabola y=x^(2)-6x+6 which is perpend...

    Text Solution

    |

  3. If the normals at two points P and Q of a parabola y^2 = 4ax intersect...

    Text Solution

    |

  4. If the point (at^2,2at) be the extremity of a focal chord of parabola ...

    Text Solution

    |

  5. A triangle ABC of area Delta is inscribed in the parabola y^2 = 4ax s...

    Text Solution

    |

  6. The locus of the middle points of the focal chord of the parabola y^(2...

    Text Solution

    |

  7. The locus of the poles of focal chords of the parabola y^2 = 4ax is

    Text Solution

    |

  8. A focal chord of parabola y^(2)=4x .is inclined at an angle of (pi)/(4...

    Text Solution

    |

  9. The length of the subnormal to the parabola y^(2)=4ax at any point is ...

    Text Solution

    |

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

    Text Solution

    |

  11. The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k...

    Text Solution

    |

  12. If the normals any point to the parabola x^(2)=4y cuts the line y = 2 ...

    Text Solution

    |

  13. The locus of the mid-points of the portion of the normal to the parabo...

    Text Solution

    |

  14. Through the vertex O of a parabola y^2 = 4x chords OP and OQ are draw...

    Text Solution

    |

  15. Tangents are drawn from any point on the line x + 4a=0 to the parabola...

    Text Solution

    |

  16. A is a point on the parabola y^2 = 4ax The normal at A cuts the parabo...

    Text Solution

    |

  17. The length of the normal chord to the parabola y^2 = 4x which subtends...

    Text Solution

    |

  18. A variable chord PQ of the parabola y^2 = 4ax subtends a right angle ...

    Text Solution

    |

  19. The locus of point of intersection of two normals drawn to the parabol...

    Text Solution

    |

  20. P ,Q , and R are the feet of the normals drawn to a parabola (y-3)^2=8...

    Text Solution

    |