Home
Class 12
MATHS
The tangents at the points (a t(1)^(2), ...

The tangents at the points `(a t_(1)^(2), 2 a t_(1)), (a t_(2)^(2), 2 a t_(2))` are right angles if

A

`t_(1) cdot t_(2)=-1`

B

`t_(1) cdot t_(2)=1`

C

`t_(1) cdot t_(2)=2`

D

`t_(1) cdot t_(2)=-2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • Pair Of Lines

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|129 Videos
  • PERMUTATION AND COMBINATIONS

    HIMALAYA PUBLICATION|Exercise Question Bank|104 Videos

Similar Questions

Explore conceptually related problems

If t_(1), t_(2) and t_(3) are distinct, then the points: (t_(1), 2at_(1), at_(1)^(3)), (t_(2), 2at_(2)+at_(2)^(3)) and (t_(3), 2at_(3)+at_(3)^(3)) are colinear if :

If x = 2/t^(2), y = t^(3)-1, (d^(2)y)/(dx^(2) ) =

The slope of the tangent to the curve x = t^(2) + 3t - 8, y = 2t^(2) - 2t - 5 at the point (2,-1) is

A tangent at any point on the ellipse (x^(2))/(9)+(y^(2))/(4)=1 is cut by the tangents at the extremities of the major axis at T_(1)andT_(2) . The circle on T_(1)T_(2) as diameter passes through the point :

The correct relationship between the boiling points of very dilute solutions of AlCl_(3) (t_(1)) and CaCl_(2)(t_(2)) , having the same molar concentration, is

The point of extremum of the function phi (x) = int_1^(x) e^(t^(2)/2) (1-t^(2)) dt are

Find the matrices of transformation T_(1)T_(2) and T_(2)T_(1) when T_(1) is rotated through an angle 60^(@) and T_(2) is the reflection in the Y-asix Also, verify that T_(1)T_(2)!=T_(2)T_(1).

If the normals at points ' t_(1) " and ' t_(2) ' to the parabola y^(2)=4 a x meet on the parabola, then

HIMALAYA PUBLICATION-PARABOLA-QUESTION BANK
  1. If 2y = 5x + k is a tangent to the parabola y^(2) = 6x then k =

    Text Solution

    |

  2. The focus of the parabola y^(2)-4 y-8 x+4=0 is

    Text Solution

    |

  3. The tangents at the points (a t(1)^(2), 2 a t(1)), (a t(2)^(2), 2 a t(...

    Text Solution

    |

  4. Focus of the parabola y^(2)-8 x-32=0 is at

    Text Solution

    |

  5. The directrix of the parabola y^(2)=16 x is

    Text Solution

    |

  6. The vertex of the parabola y^(2)=5 x+4 y+1 is

    Text Solution

    |

  7. The axis of the parabola 2 x^(2)+5 y-3 x+4=0 is

    Text Solution

    |

  8. The tangents drawn at the extremities of a focal chord of the parabol...

    Text Solution

    |

  9. A parabola has its focus at (-4,0) and its directrix is x=4 . Its equa...

    Text Solution

    |

  10. If two tangents drawn from a point p to the parabola y^(2)=4x are at r...

    Text Solution

    |

  11. If y=2 x+k is a tangent to y^(2)=8 x, then k=

    Text Solution

    |

  12. The equation of the parabola whose vertex is (1,-2) and focus is (1,-1...

    Text Solution

    |

  13. Focus of the parabola (y-2)^(2)=20(x+3) is

    Text Solution

    |

  14. Two perpendicular tangents to y^(2)=4 a x always intersect on the line

    Text Solution

    |

  15. Equation of the tangent at (-4,-4) " on " x^(2) = -4y is

    Text Solution

    |

  16. The vertex of the parabola (y-2)^(2) = 16(x-1) is

    Text Solution

    |

  17. Equation of the parabola with its vertex at (1,1) and focus (3,1) is

    Text Solution

    |

  18. The equation to the parabola whose focus is (1,-1) and the directrix i...

    Text Solution

    |

  19. The directrix of the parabola x^(2)-4x-8y+12=0

    Text Solution

    |

  20. If(0, 6) and (0,3) are respectively the vertex & focus of a parabola t...

    Text Solution

    |