Home
Class 12
MATHS
In the parabola y^(2) = 4ax, the tangent...

In the parabola `y^(2) = 4ax`, the tangent at the point P, whose abscissa is equal to the latus ractum meets the axis in T & the normal at P cuts the parabola again in Q. Prove that PT : PQ = 4 : 5.

Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    MOTION|Exercise EXERCISE - IV|33 Videos

  • PARABOLA

    MOTION|Exercise EXERCISE - II|17 Videos

  • MONOTONOCITY

    MOTION|Exercise Exercise - 4 ( Level-II ) Previous Year (Paragraph)|2 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

Similar Questions

Explore conceptually related problems

In the parabola y^(2)=4ax, then tangent at P whose abscissa is equal to the latus rectum meets its axis at T, and normal P cuts the curve again at Q. Show that PT:PQ=4:5

The normal meet the parabola y^(2)=4ax at that point where the abscissa of the point is equal to the ordinate of the point is

The normal at P(8,8) to the parabola y^(2)=8x cuts it again at Q then PQ

If "P" is a point on the parabola " y^(2)=4ax " in which the abscissa is equal to ordinate then the equation of the normal at "P" is

Let p be a point on the parabola y^(2)=4ax then the abscissa of p ,the ordinates of p and the latus rectum are in

IF the normal to the parabola y^2=4ax at point t_1 cuts the parabola again at point t_2 , prove that t_2^2ge8

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

MOTION-PARABOLA-EXERCISE - III
  1. From vertex O ofthe parabola y^2=4ax perpendicular is drawn at a tange...

    Text Solution

    |

  2. Let P be a point on the parabola y^(2) - 2y - 4x+5=0, such that the ta...

    Text Solution

    |

  3. Two tangents to the parabola y^(2) = 8x meet the tangent at its vertex...

    Text Solution

    |

  4. Show that the normals at the points (4a, 4a) & at the upper end of t...

    Text Solution

    |

  5. In the parabola y^(2) = 4ax, the tangent at the point P, whose absciss...

    Text Solution

    |

  6. Prove that the locus of the middle point of portion of a normal to y^(...

    Text Solution

    |

  7. Three normals to y^2=4x pass through the point (15, 12). Show that one...

    Text Solution

    |

  8. Normals are drawn from a point P with slopes m1,m2 and m3 are drawn fr...

    Text Solution

    |

  9. Prove that, the normal to y^(2) = 12x at (3,6) meets the parabola agai...

    Text Solution

    |

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

    Text Solution

    |

  11. A variable chord PQ of the parabola y^(2) = 4x is drawn parallel to th...

    Text Solution

    |

  12. Show that the normals at two suitable distinct real points on the para...

    Text Solution

    |

  13. Let S is the focus of the parabola y^(2) = 4ax and X the foot of the d...

    Text Solution

    |

  14. Prove that the parabola y^(2) = 16x and the circle x^(2) + y^(2) - 40x...

    Text Solution

    |

  15. .Find the equation ofthe circle which passes through the focus ofthe p...

    Text Solution

    |

  16. A fixed parabola y^(2) = 4ax touches a variable parabola. Find the equ...

    Text Solution

    |

  17. Show that an infinite number of triangles can be inscribed in either o...

    Text Solution

    |

  18. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

    Text Solution

    |

  19. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

    Text Solution

    |

  20. From the point P(h, k) three normals are drawn to the parabola x^(2) =...

    Text Solution

    |