Home
Class 12
MATHS
The tangent PT and the normal PN to the ...

The tangent PT and the normal PN to the parabola `y^2=4ax` at a point P on it meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose:

A

vertex= `(2a/3 ,0)`

B

directrix is `x=0`

C

latus rectum=`2a/3`

D

focus=`(a,0)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

Similar Questions

Explore conceptually related problems

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

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

TP and TQ are tangents to parabola y^(2)=4x and normals at P and Q intersect at a point R on the curve.The locus of the centre of the circle circumseribing Delta TPQ is a parabola whose

The tangent and normal at P(t), for all real positive t, to the parabola y^(2)=4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, Tand G is

From a variable point R on the line y = 2x + 3 tangents are drawn to the parabola y^(2)=4ax touch it at P and Q point. Find the locus of the centroid of the triangle PQR.

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

Tangent and normal at any point P of the parabola y^(2)=4ax(a gt 0) meet the x-axis at T and N respectively. If the lengths of sub-tangent and sub-normal at this point are equal, then the area of DeltaPTN is given by

A DAS GUPTA-Objective Tests-Exercise
  1. for 0ltthetaltpi/2 the solution(s) of sum(m=1)^6c o s e c(theta+((m-...

    Text Solution

    |

  2. In a triangle ABC with fixed base BC, the vertex A moves such that cos...

    Text Solution

    |

  3. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

  4. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  5. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  6. For the function f(x)=x "cos" 1/x, x ge1

    Text Solution

    |

  7. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  8. The area of the region bounded by the curve y=e^(x) and lines x=0 and ...

    Text Solution

    |

  9. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  10. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

    Text Solution

    |

  11. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

    Text Solution

    |

  12. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  13. If the angle A , B and C of a triangle are in arithmetic progession an...

    Text Solution

    |

  14. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |

  15. The equation of the plane containing the straight line x/2=y/3=z/4 and...

    Text Solution

    |

  16. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  17. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  18. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  19. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  20. A signal which can be green or red with probability 4/5 and 1/5 respec...

    Text Solution

    |