Home
Class 11
MATHS
If the normals to the parabola y^2=4a x ...

If the normals to the parabola `y^2=4a x` at `P` meets the curve again at `Q` and if `P Q` and the normal at `Q` make angle `alpha` and`beta` , respectively, with the x-axis, then `t a nalpha(tanalpha+tanbeta)` has the value equal to

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

The normal to the parabola y^(2)=8x at the point (2, 4) meets the parabola again at the point-

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Qa n dQ^(prime), then Q Q ' is

Prove that the normal at (am^(2),2am) to the parabola y^(2)=4ax meets the curve again at an angle tan^(-1)((1)/(2)m) .

A normal drawn to the parabola y^2=4a x meets the curve again at Q such that the angle subtended by P Q at the vertex is 90^0dot Then the coordinates of P can be

If a normal to a parabola y^2 =4ax makes an angle phi with its axis, then it will cut the curve again at an angle

If the normals at P, Q, R of the parabola y^2=4ax meet in O and S be its focus, then prove that .SP . SQ . SR = a . (SO)^2 .

If PQ and Rs are normal chords of the parabola y^(2) = 8x and the points P,Q,R,S are concyclic, then

If the normal chord of the parabola y^(2)=4x makes an angle 45^(@) with the axis of the parabola, then its length, is

Find the equation of normal to the parabola y^(2)=12x at (3t^(2),6t) . Hence, find the equation of the normal to this parabola which makes an angle 135^(@) with the x-axis.

If the line passing through the focus S of the parabola y=a x^2+b x+c meets the parabola at Pa n dQ and if S P=4 and S Q=6 , then find the value of adot

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. PQ is a normal chord of the parabola y^2 =4ax at P, A being t...

    Text Solution

    |

  2. If two normals to a parabola y^2 = 4ax intersect at right angles then ...

    Text Solution

    |

  3. If the normals to the parabola y^2=4a x at P meets the curve again at ...

    Text Solution

    |

  4. If a leaf of a book is folded so that one corner moves along an opp...

    Text Solution

    |

  5. A parabola of latus-rectum 1 touches a fixed equal parabola. The axe...

    Text Solution

    |

  6. A movable parabola touches x-axis and y-axis at (0,1) and (1,0). Then ...

    Text Solution

    |

  7. Let N be the foot of perpendicular to the x-axis from point P on the p...

    Text Solution

    |

  8. Two lines are drawn at right angles, one being a tangent to y^(2)=4ax ...

    Text Solution

    |

  9. The area of the trapezium whose vertices lie on the parabola y^2 = 4x ...

    Text Solution

    |

  10. Find the range of parameter a for which a unique circle will pass thro...

    Text Solution

    |

  11. Find the radius of the largest circle, which passes through the focus ...

    Text Solution

    |

  12. A tangent is drawn to the parabola y^(2)=4ax at P such that it cuts th...

    Text Solution

    |

  13. Tangents are drawn to the parabola at three distinct points. Prove t...

    Text Solution

    |

  14. Statement 1: The circumcircle of a triangle formed by the lines x=0,...

    Text Solution

    |

  15. Statement 1: The point of intersection of the tangents at three dist...

    Text Solution

    |

  16. Statement 1: If the straight line x=8 meets the parabola y^2=8x at Pa ...

    Text Solution

    |

  17. Statement 1: Normal chord drawn at the point (8, 8) of the parabola ...

    Text Solution

    |

  18. Statement 1: The value of alpha for which the point (alpha,alpha^2) li...

    Text Solution

    |

  19. Statement 1: If there exist points on the circle x^2+y^2=a^2 from whic...

    Text Solution

    |

  20. Let L be a normal to the parabola y^(2)=4x. If L passes through the po...

    Text Solution

    |