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The tangent PT and the normal PN to the parabola y2 = 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(2009)
  • a)
    vertex is
  • b)
    directrix is x = 0
  • c)
    latus rectum is 
  • d)
    focus is (a, 0)
Correct answer is option 'A,D'. Can you explain this answer?
Most Upvoted Answer
The tangent PT and the normal PN to the parabola y2 = 4ax at a point P...
Tangent is Y=x/t+at
normal is Y+xt=2at+at^3
so on y=0 we get point T& N
we know point p(at^2,2at)
so we can easily find centroid in term of t & then eliminate t
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Community Answer
The tangent PT and the normal PN to the parabola y2 = 4ax at a point P...
Let P(at2 , 2at) be any point on the parabola y2 = 4ax.
Then tangent to parabola at P is  
which meets the axis of parabola i.e x-axis at T (– at2, 0).
Also normal to parabola at P is tx + y = 2at+ at3 which meets the axis of parabola at N (2a + at2 , 0)
Let G (x, y) be the centriod of Δ PTN , then
Eliminating t from above, we get the locus of centriod G as
which is a parabola with vertex  directrix as
latus r ectum as   and
focus  as (a, 0).
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The tangent PT and the normal PN to the parabola y2 = 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(2009)a)vertex is b)directrix is x = 0c)latus rectum isd)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer?
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The tangent PT and the normal PN to the parabola y2 = 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(2009)a)vertex is b)directrix is x = 0c)latus rectum isd)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The tangent PT and the normal PN to the parabola y2 = 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(2009)a)vertex is b)directrix is x = 0c)latus rectum isd)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The tangent PT and the normal PN to the parabola y2 = 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(2009)a)vertex is b)directrix is x = 0c)latus rectum isd)focus is (a, 0)Correct answer is option 'A,D'. Can you explain this answer?.
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