Home
Class 11
MATHS
If normal to parabola y^(2)=4ax at point...

If normal to parabola `y^(2)=4ax` at point `P(at^(2),2at)` intersects the parabola again at Q, such that sum of ordinates of the points P and Q is 3, then find the length of latus ectum in terms of t.

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 normal to the parabola y^2-4a x=0 at alpha point intersects the parabola again such that the sum of ordinates of these two points is 3, then show that the semi-latus rectum is equal to -1. 5alphadot

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2^2 geq8.

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

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

The parabola y^2=4ax passes through the point (2,-6). Find the length of the latus rectum.

The normal to the parabola y^(2)=4ax at P(am_(1)^(2),2am_(1)) intersects it again at Q(am_(2)^(2), 2am_(2)) .If A be the vertex of the parabola then show that the area of the triangle APQ is (2a^(2))/(m_(1))(1+m_(1)^(2))(2+m_(1)^(2)) .

The parabola y^(2) =- 4ax passes through the point (-1,2) . Find the coordinates of its focus and length of latus rectum.

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. The length of the latus rectum of the parabola whose focus is a. ((u...

    Text Solution

    |

  2. If parabolas y^(2)=lamdaxand25[(x-3)^(2)+(y+2)^(2)]=(3x-4y-2)^(2) are ...

    Text Solution

    |

  3. If normal to parabola y^(2)=4ax at point P(at^(2),2at) intersects the ...

    Text Solution

    |

  4. The set of points on the axis of the parabola y^2=4x+8 from which the ...

    Text Solution

    |

  5. Which one of the following equation represent parametric equation to a...

    Text Solution

    |

  6. The vertex of a parabola is the point (a , b) and the latus rectum is ...

    Text Solution

    |

  7. The curve represented by the equation sqrt(p x)+sqrt(q y)=1 where p ,q...

    Text Solution

    |

  8. Prove that the equation of the parabola whose focus is (0, 0) and tang...

    Text Solution

    |

  9. The equation of the parabola whose vertex and focus lie on the axis of...

    Text Solution

    |

  10. Prove that for a suitable point P on the axis of the parabola y^(2)=4a...

    Text Solution

    |

  11. Two parabola have the same focus. If their directrices are the x-and t...

    Text Solution

    |

  12. The number of common chord of the parabolas x=y^(2)-6y+11andy=x^(2)-6x...

    Text Solution

    |

  13. Find the equation of the curve whose parametric equations are x=1+4c...

    Text Solution

    |

  14. Prove that any point on the ellipse whose foci are (-1,0) and (7,0)...

    Text Solution

    |

  15. Find the eccentric angle of a point on the ellipse (x^2)/6+(y^2)/2=...

    Text Solution

    |

  16. Find the area of the greatest rectangle that can be inscribed in an ...

    Text Solution

    |

  17. The auxiliary circle of a family of ellipses passes through the ori...

    Text Solution

    |

  18. Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

    Text Solution

    |

  19. A line passing through the origin O(0,0) intersects two concentric ...

    Text Solution

    |

  20. If the line l x+m y+n=0 cuts the ellipse ((x^2)/(a^2))+((y^2)/(b^2)...

    Text Solution

    |